Whose? Jussie's fingerprints on something he owned? Or is the assertion meant to be that he faked the whole thing but still actually had bleach dumped on himself by those guys, leaving traces of their fingerprints (because they were somehow not wearing gloves on one of the coldest nights of the year), and then took it back from them? Is that why fingerprints would matter?
I'm not saying that's totally impossible and could never happen, but I would say it's a lot weirder than the original assertion that a black man was assaulted on the street that people found so outrageous and unbelievable that they immediately had so many questions, so it's a little weird that it's just being presented as obviously suspicious and relevant that a person would have a standard cleaning product in their own home.
Also I think you're underestimating how long it takes to run fingerprints, although I suppose this case is high profile enough everything is being fast tracked.