The actual quote from page 34 of the Europe rules is, “Loading onto and/or offloading from a transport counts as a land unit’s entire move; it can’t move before loading or after offloading.” The “and/or” means the phrase is read as both “Loading onto and offloading from” and “Loading onto or offloading from”, which indicates that whether a unit loads, offloads, or both it uses its entire move for the turn. As a result, infantry may both load and offload in the same turn (provided they belong to the same power as the transport).
Which makes perfect sense, because for US troops to load onto, and then off of, a UK transport, for example, it would imply a move by the UK transport, which it obviously can’t do on the US’s turn.
It’s the same reason a US transport can’t bridge US troops into a land combat and then move to another sea zone during the non-combat phase: it’s MOVE has been used up. However, US troops could load onto (but not subsequently off) a US transport during combat, and then the transport could move during non-combat with the troops on board, because it’s move hasn’t been used up. The act of bridging, however, implies a move - whether combat or non-combat - has been made.