Not correct. There was no exemption from Federal Motor Vehicle Safety Standard 209 (seat belt assemblies) for "commercial vehicles" -- it sounds like you might have read somebody's misunderstanding of the reason why school, transit, and tour buses aren't required to have seat belts for the passengers.
FMVSS 209 was the first US national vehicle safety standard to take effect, on 1 March 1967. Under FMVSS 209, shoulder belts at each front outboard seating position became mandatory in new passenger vehicles built on or after 1 January 1968. That's "passenger vehicle" as defined in the standard -- some trucks and vans weren't considered passenger vehicles for the purpose of the standard, but no, it is definitely not the case that a passenger car would be exempt from the requirement simply because it was a fleet car, a taxi, or bought for some other commercial purpose.
Shoulder belts were optional equipment in Chrysler Corp vehicles, including A-bodies, as early as 1966. They were standard equipment in Chrysler Corp vehicles made and sold in some other countries even earlier than that. For example, Swiss-built and Australian-built Valiants got nicer, better seat belts considerably earlier than US/Canada cars. In the US/Canada A-bodies, the front shoulder belts were completely separate from the lap belts (with their own buckles -- a total of five buckles making a mess all over the front seat!) through 1971. In 1972 the lap and shoulder belt end fittings were redesigned so they could be clipped together and one single tongue was then fastened into one single buckle. In 1974 was released the "Uni-Belt", Chrysler's name for the now-familiar single belt/single-buckle retractable 3-point belt.
