It seems odd that it would be this much of a challenge, but the missiles the planes are carrying target heat sources, and there wasn't enough of a heat source on the balloon. And the problem with using guns is that at 65,000 feet the helium would escape so slowly the damn thing would be halfway to Europe before it came down. (not sure why they couldn't just shred it with a GAU... but I'm not sure we have anything in inventory that flies at 65,000 feet)
I would guess it's a problem that can be solved, but it seems to be one we hadn't thought of until recently.