One thing we can all agree on is that you should have your insurance in place before you travel. You have absolutely no guarantee about what sort of maltreatment your luggage is going to have to deal with. That having been said, I have never ever experienced a real problem when flying with a guitar -- the worst that ever happened waa that it came a couple of days late (OK, that *might* have been serious) because it went to the wrong airport.
The 'loosen your strings' thing is something I have heard (and had heard 30 years ago) so there might be something in it. But the only time I had a guitar actually *do* what's advertised was when it had been sitting at home and had not been touched for several weeks (opened the case and the bridge had self-detonated...)