Neither the Marines nor Sailors have retained their former "river crossing" attribute. That attribute has been given to the Pontooneer support units.
The Amphibious attribute which Marines and Sailors now have is a unit-attribute, much like the Strong Morale attribute

that the Flavor units have. It only counts for the unit.
If a Marin is embedded in a division, that is the unit in which it is contained and that division will benefit from the Marines Amphibious attribute.
Basically, when you land from ships or cross a major river versus an opposing force (not necessarily advisable :blink

at least the first round of battle (until your force has gained 10% MC?) your force is at a great disadvantage. With the Amphibious attribute your force only suffers 50% of that disadvantage.
Once your landing force had gained a bridgehead (10% MC) other units may follow and do not suffer the landing-penalty.
That's what Marines are good for-- aside from them being elite-- and having a high level of cohesion-- and being generally bad-ass .....
