I apologize for assuming you hadn't seen the videos. And absolutely it makes sense that if you're guilty of a crime to clam up, because there's no sense in making it easier for the prosecutor.
However, if you're innocent, haven't done anything, what do you have to fear? Sure, the chances are extremely slim that they're going to arrest the wrong guy, but it DOES happen, and what happens once they've arrested someone for a crime? Any further investigation and search for suspectsSTOPS at that point, unless you can be exonerated and then they'll start looking again.
So in your case, what if he checked your shoes and they JUST happened to MATCH whatever he was looking for? What if your innocent answers to his questions put you near the location of the crime? You allowed a search with no reasonable suspicion, and only added more evidence to the case against you by admitting you were in the vicinity. NOW they've wrongly arrested their suspect and you helped them do it.
I'm sure it's an extremely rare case that someone gets wrongly arrested, that even less are prosecuted, and even fewer of those are actually convicted, but it DOES happen, and I'm not willing to take that chance by helping it happen.
I like the idea of answering any questions with a question. "Are you investigating a crime, officer?" Find out what they ARE looking for before telling them anything. It may be that they're investigating a robbery at the Shop'N'Go that I just drove by 5 minutes ago, and I sure as hell am not going to tell them I was anywhere in the area...
I do agree with one of the previous posters that it really does depend on the circumstances. I understand the police have a job to do investigating crimes, but assisting them withsolving a crime falls much lower in priority to covering my own rear end. When in doubt, I'm not going to take the chance of somehow accidentally incriminating myself for something I didn't do.