Well as far as the gun cabinet if it is that dirty and he doesn't do any cleaning or proper storage of his firearms I am sure they all could use some TLC.
As for the 30-06... i have a savage 30-06 and with proper sighting in, good optics, trigger adjusted, good loads to shoot I am sure you could hit a ground hog but at 300yards it would be a good shot for sure.
It also sounds to me that he maybe stretching the truth a bit. Alot of hunters have a hard time hitting a deer at 300 yards with a properly setup gun let along someone who never cleans or shoots a pre WWII gun.

Take him out and have him shoot a ground hog at 300 yards with you there and then you will see for yourself.