I'm not in the US, so maybe things are very different here, but I still wonder if the absolutist advice is helpful in situations like this:

One night, while walking, I was stopped by police because I roughly matched the description of someone who had burgled a house nearby. They didn't tell me this straight away; they just asked who I was, where I lived, and what I was doing. I didn't have ID on me, but I answered their questions honestly. They went to their car for a bit (presumably checking that my name matched my address and/or that I didn't have a record), then came back, explained the situation, and let me go as they had no strong reason to suspect me. The whole interaction was pretty relaxed and cordial, and they didn't contact me again.

Things definitely wouldn't have gone better for me had I made a point of refusing to engage beyond the legally required minimum, and it's easy to imagine how they could have gone significantly worse.

It definitely depends on the country. I live in Scotland and I've been perfectly happy to chat with police officers but if I'm taken in for questioning (which in Scotland is an arrest) I would have no hesitation in asking for a solicitor and they would probably advise no comment on every question.

If I want to help them out I would then prepare a written statement, approved by my solicitor, and give them that.

It's just the sensible way to go.

There's no rush. Take your time and be smart.