There's a radio up by that grave too, and I got the feeling that someone (Ulysses) spent time at the gravesite. Like he was mourning a loved one. Your observations are pretty convincing. "Served" sounds right.
Ok, this is -pure- speculation now, but:
We
know Caesar lies to his people. To keep them ignorant, to keep them loyal, to gain power. What if, the reason Ulysses was so surprised to see the Courier was alive, was because Caesar had lied to him? What if Caesar had, to gain Ulysses' loyalty, promised the death of the Courier? Thus, when Ulysses saw his name, he lost all trust in Caesar, and that's why he was willing to pass up on such an important secret operation for Caesar's Legion.
I say this simply because Ulysses quote on the collector's edition cards is "The day I set my flag down, it'll be over my body or over a nation I believe in." Sounds very patriotic for a guy who single-handedly ruined a Frumentarii job to get the Platinum Chip. That's why I argue that there must be some reason for him to ditch them like that, and this to me makes the most sense with what info we've been given so far. Ties in with Caesar's habit of lying, with Ulysses' assumed patriotism and work for the Legion, and his surprise at seeing the Courier is alive. It would shatter his trust.
I'll admit it's not flawless. You'd expect Caesar to at least do some form of double-take when he first meets you, this still doesn't explain why Ulysses wants the Courier dead (supposedly) and most importantly, I can't come up with an explanation as to why Caesar would want to win Ulysses trust and loyalty so dearly that he'd bother to lie about killing the Courier. Just a thought though.