I had a quick look through the Bolt Action catalogue (German and British) and the head counts match the Bolt Action ones on your list. Is it other brands where the head counts vary?
Looking at the Osprey books for the Vickers and the MG34/42, they appear to have a crew of three (the latter on a tripod as a Bolt Action MMG).
I suspect that the Bolt Action head counts are just that, based partly on research and partly on game play (they all have a consistent head count independent of nationality - if a machine gun starts with four crew it is an HMG).
Warlord have repackaged some figures so they better match the rules, I cannot remember if that included the weapon teams.
Operation Squad has a four men operating a Soviet 81mm mortar, other head counts match Bolt Action.