What JR said. I would hazard a guess that the design intent behind the rule was that armoured halftracks, as used by the Germans and Americans, were intended as not just troop transports but as actual integral members of the combat team, i.e., they're there to fight with and as part of the infantry. Other vehicles that may be present on the battlefield may be there to support the infantry but are not necessarily with the infantry.
Of course that's a gross over-simplification and is not going to be true of all nations at all times. A scenario designer is always free to include an appropriate SSR if he feels the situation warrants it. But as JR says: so far as the rules are concerned, if it's not an armoured halftrack (or Carrier), then it's not an armoured halftrack (or Carrier).
(Of course the vehicle note for any specific vehicle type may state an explicit EXC, which is why you always need to check the vehicle notes.)