I see nothing in that statement that could translate into "Iwata said that if Wii hadn't been successful, Nintendo would have pulled out of the home console business".
As you've written afterward Iwata just said that Nintendo shouldn't be in the console business if their internal target is to just outsell the GC (measly 20M units) which of course is obvious.
The reason why DS/Wii were of special importance is another (Nintendo could have released other consoles even if DS/Wii disappointed).
In the mind of the Nintendo's management the philosophy behind DS/Wii traced a template which take advantage of the company's unique skill set and that could be replicated in the future to give Nintendo again a prominence role in the videogame industry.
This is the true meaning behind this statement by Hiroshi Yamauchi:
The executive said that Nintendo will "give [its] all" to promote the Nintendo DS. He conceded that the device may not immediately overwhelm audiences, but that he hopes it will help ring in a new era, which may revitalize the games industry. "If we are unsuccessful with the Nintendo DS, we may not go bankrupt, but we will be crushed. The next two years will be a really crucial time for Nintendo."
Despite what some people seem to think, Nintendo can't afford back-to-back-to-back-to-back failures. Nintendo's shareholders would never allow it. Nintendo's piggybank will never be smashed to buy that thing that the fans want. Money is always supposed to go into Nintendo's piggybank, not ever come out of it. It's a black hole of wealth.
The idea that Nintendo could continually lose money just because they are cash rich is indeed stupid.
Nintendo's management always acted with business savviness, they will try to reinvent Nintendo if a repeated cycle of consoles failures happen.
Nintendo doesn't like to talk about it, but the N64 was a failure. It was a "conservative" failure (sort of like the Virtual Boy), because Nintendo didn't spend a lot of money on it's CD drive (which was part of why it failed), and Nintendo fell into incredible success with Pokemon on the GameBoy, so that kept Nintendo's head above water, but N64 was a failure. Especially in Japan (where Nintendo places a lot of importance). Iwata was brought on board in GameCube's design stages primarily to try and repair Nintendo's extremely damaged Japanese third party relations.
N64 was certainly a troubled console.
However the theory that say that what made Nintendo profitable during the N64 era was only Pokemon isn't supported by the data available (operating income in the years before the introduction of Pokemon in the west, first-party software sales on N64).
But GameCube, despite it's hugely repaired Japanese third party relations, despite it's fiscally conservative design, despite it's great game sales numbers (relative to it's low hardware sales numbers), despite the massively successful GameBoy Advance picking up a lot of the GameCube's slack... the GameCube was an even bigger failure than the N64.
GC era was the darkest era for Nintendo since when they entered the videogame business, it was an even worse period than the WiiU/3DS era with its three consecutive yearly losses (first yearly losses ever recorded by Nintendo since entering the videogame business).
The reason is that Sony hit the market (and Nintendo) with a paradigm shift during the N64 era.
The questions that arise during that time should have been of this kind:
Is the first-party driven business model a relic of the past?
How can we counter a console maker who center its business on receiving the best and most third-party support when our strong point and whole business model focus on first-party games? (it was a many vs one dilemma)
How can we counter conglomerates which can leverage far more resources than a simple gaming company can?
The plan elaborates for the GC and that originated from the questions above was totally wrong and betrayed a misunderstanding on what really defines Nintendo. They tried to imitate Sony and designed the GC in a way that it was easy to develop games for and struck deals with specific third-parties (japanese ones for the most part).
This of course couldn't work because Nintendo's core strength isn't attracting third-party support and never will.
It didn't matter that GC was priced at $99 since September 2003 because price was never the issue (it was the value!).
The solution that correctly answered the questions above were elaborated for DS and Wii.
Is the first-party driven business model a relic of the past? Maybe but Nintendo has the strongest first-party in the world and they can leverage it to prove new concepts. Nintendo is a unique case.
How can we counter a console maker who center its business on receiving the best and most third-party support when our strong point and whole business model focus on first-party games? (it was a many vs one dilemma)
How can we counter conglomerates which can leverage far more resources than a simple gaming company can?
For third-party driven model to work it need to offer a standard platform (third-party publishers hate unproven concepts that don't have already proven templates on how making profits out of it).
A first-party driven model doesn't have this limitation because with this business model first-party games have higher priority over third-party games, it's the first-party software that need to generate enough momentum to make the platform successful.
So a first-party driven console manufacturer like Nintendo can introduce unconventional hardware design and prove it to the market using its first-party software (it's the software that sell the console but the software act in tandem with the hardware).
However these unconventional hardware designs shouldn't be different just for the sake of being different but they need to serve meaningful purposes (this was the main issue for WiiU and 3DS together with the high hardware cost).
The meaningful purpose served by DS/Wii was introducing interfaces with a low barrier of utilization and software that use them so that even people that were scared by the complexity of the standard control pads could play videogames.
The meaningful purpose served by the Switch is to let people with a busy life to enjoy videogames wherever, whenever and how they want (this was achieved with a modular design).
Instead of following Sony, Nintendo just double down on what make Nintendo special.
And the 3DS (while not a failure) wasn't in any position to bail anyone out.
It's often forgotten that 3DS was certainly responsible (at least in big part) of the losses incurred by Nintendo in the 3DS/WiiU era.
The first yearly loss was in the fiscal year when Nintendo decided to drastically reduce the 3DS price, six months after the launch.
But then, the Switch turned things right back around again. That lifted the pressure and Nintendo's failures can once again be forgiven. If Switch had failed though, Nintendo could have easily joined Sega and pulled out of the console race. Nintendo is clearly not in as bad of a position as Sega right now, but that's due to the Switch and Dreamcast (and how different those two were), not the WiiU and Saturn (and how alike those two were).
Both Nintendo and Sega had the same challenges to face up once Sony triggered the paradigm shift (the questions above).
However Nintendo and Sega were different companies with different situations, different backgrounds, different cash balances, different first-party software strengths and different business acumen.
In short Nintendo was in a much better spot than Sega ever was.
Note that while WiiU failed it didn't disprove the business template Nintendo used since after the GC.
The leveraging of the unique hardware/software integration (which favorably play at Nintendo core strengths) is what brought Switch to success.