312 is close enough. The yield strength of a lead core bullet is far less than the 45,000 psi kick in the ass it gets. It gets rammed into the rifling very hard and will fit tight.
The only limit on undersized bullets is if a bullet is too small you can get gas cutting. 1 thou is no problem.
Don't forget the steel barrel is quite elastic and it expands when the round is fired. For the first inch or two the barrel is quite a bit bigger, and the bullet expands with it, and then gets swaged back down by the 4 inch point.
I have watched barrels photographed with high speed x-rays. The barrel looks like a snake swallowing a rabbit for the first few inches.
I am sure there are members here who can calculate the expansion given the pressure and modulus of elasticity. It is a lot more than 1 thou.