I don't know that it is hair-splitting, and if it is, it's splitting the definition where it deserves to be split.

People call a US civilian model AR15 an "assault rifle" which it is not. It is capable of semiautomatic fire only. This is directly on point to the discussion.

The assault weapon is capable of "select fire," which may or may not mean fully automatic in nature. Some of them use a three-round burst, but that is still a machine gun (actually, the BATFE term is "machinegun") because it can shoot more than one round with one pull of the trigger.

But as you state, select fire is not the only defining characteristic of an assault weapon. A .50 BMG certainly does not qualify.