There is a quote somewhere in the books that I'll bring here from memory:
If 15% of people from Earth would decide to go beyond the rings, we would have maybe a bit more living space. If 15% of people from Mars would do the same, we can forget about terraforming.
This means that in Martian society, everyone is important - there is no room for unemployment because everyone has to do it's part one way or another. From the military perspective, that forced Mars to create highly advanced technology, that allowed them to compete with Earth numerical superiority (someone compared it to the situation similar to Germany and USSR during the WW II). Still, even those highly advanced spaceships, even those Marines need humans to control them.
So when Martians started emigrating through the Rings, their government was forced to offset those missing people by taking them from somewhere, and since the relationships with Earth are better than they were, the Navy was the obvious source.