Definitely try the open sights before getting too worked up over it.
Pivot-lockup is the latch mechanism that keeps the breach closed. It has a spring-loaded wedge, and this is what you are overcoming when you break the barrel open to get to the breach to load a pellet and start cocking the gun.
If the breach lock-up isn't tight, there's one of 2 things that can happen.
First, the breach might lock-up in a slightly different position (either up and down or side to side) each time you close the barrel. Obviously, with a scope, this kills any accuracy. It is less an issue with the open sights which sit on the barrel, and therefore always point where the barrel is pointed.
Second, the breach might move when the gun is fired. This'll screw up shooting with either a scope or with opens.
Does the barrel seem to have any easy "free play" when it is closed? After you cock the gun but before you close the breach, is the barrel free to swing back and forth, or does the joint still feel snug?
Generally speaking, Gamo lock-up mechanisms are pretty solid. I'd be surprised if that was the problem (it's more believable on a Quest). But again, shoot it with the opens and see what it does.