I've talked myself out of more than one situation, I'm speaking from personal experience here. One incident, I was target shooting in the middle of a forest where hunting is legal, and I was called out of the forest by sirens and a loudspeaker only to be harassed by two OPP officers - I had permission to be there (from the MNR who said that exact location was FINE for target shooting), but since it wasn't in writing, according to them they could seize my firearm, charge me with reckless discharge, blah blah not going to get into the story, but I ended up walking away, with my rifle slung over my shoulder with no charges or anything bad happening, because I simply talked to them and gave them my side of the story. Funny part is, they never even walked out to my shooting location - it could have very well been dangerous, I could have been hunting out of season, but they were too lazy to even walk back to look! They walked back and forth looking at the signs on the road to see if they could find anything about hunting or firearms to see if they could come up with a bogus charge but.... nothing. It was annoying to stand there and talk to them when I knew I didn't do a thing wrong, but in that situation it was better than the alternative.
So I agree that it depends on the situation, sometimes it's better to say nothing, sometimes it helps to fill them in, they only know what they've been told.