As I see it, you have two avenues on the job, and both involve the final customer.
First off, most jobs have a 'retention' that is not paid by the customer to the GC until AFTER all the subs have been paid. You simply don't give the GC a release, and inform the customer why not.
(Sure, GC's love to try to pay you after they have received the retention, but that's not the job they agreed to!0
The second is to file a claim / lien on the property. That's what liens ar for. Many a sub (or supplier) has forced a customer to pay twice - once to the GC, and once to the sub directly. Most often the customer has a retention, or other means to pressure the GC.
All the GC has in his corner is the hammer of "future work." That's not likely to be worth having, if you won't be paid for it.
As for the "my guy wasn't authorised ..." red herring, that's the sort of things lawyers have fun with. If it's the same guy signing for materials, signing time sheets, scheduling crews, etc ... lots of luck with that one. The guy's blowing smoke - and that's a good reason to not do business with him ever again.
I can't speak for others, but I'm in the trade to MAKE things, not to debate them. I really have no desire to deal with game-playing hacks. Oddly enough, the game-playing always seems to come from two types of guys: the guy who has given all manner of other clues that he's not the most professional operation (lack of equipment, poor scheduling, 3rd-rate crew, etc.), or the "Big Corporation" that practically answers their phone with 'we're big, you're little, so kiss our tuckuss, you serf.' In either case, you've been warned.