I think they do have the general location, they keep mentioning two lakes near the base. So I suspect it's at the bottom of one of them, although then it's odd they are asking for public help finding them.
"Dagobah" was how I heard the search area described. Or parts of it at least. "The weather was horrible" when the pilot ejected, so if it was pouring rain and slipped nicely into a swamp somewhere - and then the rain doused anything smoking...
It's not too odd to ask for help. Generally they want anyone who heard/saw something to report what they saw. I witnessed a jet crash once. Even though I was a kid and they knew the exact location, they still wanted the information. If it did crash into a lake, it's possible someone heard it while they were fishing or something.
