Actually, probably not. This used to be a common dodge, but the rules have been tightened in many if not all states, and trucks must now be licensed for at least as much as their name-tag GVW.
If and how rental companies rent >26K lbs trucks, I do not know. From past experience, I know that the rental fleets have large amounts of voluminous box trucks rated at 25,999 lbs.
But getting back to the initial premise, here are the Federal regulations:
Definitions. - Federal Motor Carrier Safety Administration
which clearly define a commercial vehicle as one based on the manufacturers GVW and one working in commerce. There used to be a huge variation in chauffeur license requirements throughout the states, but the US Federal Motor Carrier Administration and the DOT, using interstate commerce as their leve, have made these much more uniform. This effort started during the Reagan administration.