Improper inflation, possibly by a loose valve/slow leak, could cause a flat eventually. That would be more of a routine maintenance issue, as you suggest.
Was there a nail in the tire? Machine screw? Sharp stick? Cracked or bent rim? There are lots of things that can make a tire go flat. It's still your word against theirs, without some sort of proof. Did you take pictures of the bad tire? The onus is clearly on the owner to get the required proof for GS Tires.
These tire warranties (and those fabulous 3rd party after market warranty ones) are probably best avoided, as they don't make any money if they paid out more on every claim, than the premiums bring in. Some claims will just be refused based on the fine print you mentioned.
I like Good Sam Roadside, they've done pretty good for me, but wouldn't consider the tire policy for many reasons. Case in point?
Buy your tires from America's Tire/Discount Tire and they'll take care of you. If there isn't a manufacturer's road hazard coverage sold with the tire, they'll offer you one, and prorate the cost of the replacement tire based on tread depth and wear. I think Michelins sold by them automatically get road hazard prorata coverage. Just get Good Sam to tow you to them, they're everywhere.
