Well, when we were scouting out the Oracle's place, we saw a guy with long hair and the 'sludge' on the floor that Celsius was being suspicious about.
Melitus obviously knows a lot more than he let on--that's pretty clear. Just the fact that when we were talking to him we weren't able to be found in the Matrix shows this. Like Burn said, maybe he's a program. Or an unknowing pawn of the system. Or something like that.
That was something you could have asked him about actually- what he wanted with it.
But yes, raises a few points. Do you think he was after it for its conventional use (police codes), or for the same use as you?
One thing for sure- you are right in that there is zero chance he would be after it if he were part of the system.
In fact, the Agents were far more keen to stop Jericho's team than you.