That's correct. Weapon DPS is purely a function of ilvl, in the same way that primary stats are.
I'm also fairly confident that all weapons of a particular type have the exact same speed now. Think that changed in either Warlords or Legion.
Yeah, weapon speed has been normalized for a while. So basically ilvl is king, with the only caveat being certain corruptions. Infinite stars is worth like 10 ilvl for example.