I'm sure I know the answer to this, but my old man is obsessing, so I told him I'd ask.

He just bought a 20ga double barrel. On the side of the barrel, it only says 3". This shotgun can shoot 2 3/4"  shells without a problem, just like you would in a 12g, right?

Absolutely,means do not exceed a 3" shell.
In shotguns the  trouble comes as an over long shell might fit in the chamber but there isn't room for the crimp to unfold completly because it is into the barrel vs the larger chamber where it should be. this will cause a huge preasure spike,shottys run on fairly low preasure and therefore have a smaller safety margin
As always ,if you own different chambered shottys be extra carefull ammo isn't mixed up.
Classic mistake is a guy who owns both 12 and 20 shottys. Extra 20 shell gets pulled out of pocket and dropped into 12 ga double gun. First time the trigger is pulled you get a click because the rim of the 20 is 3" foward at the base of the chamber. Shooter thinks he missed loading the gun somehow and loads a 12 behind th 20. Next time he pulls the trigger it gets ugly!

The only really stupid questions are the ones you don't ask!

Yeah, I figured, but felt it couldn't hurt to ask.

Thans for the quick reply.