I asked him later and he said he wanted to get the loot before everyone else so they wouldn't know how much loot there actually was.
Okay, so you've got to what he was trying to accomplish, but it doesn't sound like you've gotten to
why - and there lies the basis for the differing playstyle.
So, continue asking - Why do you want to keep loot from the other party members?
He may have a really good, role-playing answer, and you can use that understanding to build a bit of understanding among the players, and build plot.
He may simply be greedy. Then, explain to him that you and the other players really prefer a more cooperative game - it is okay to lie to , cheat, and steal from the NPCs, but not from the people who help keep his character alive. If he cannot accept this, he probably needs to find another table to play at.
If this really is a difference of play style issue, I would strongly advise against the "allow nature to take its course" route you have going here. It is a conflict
between the players, being played out by proxy within the game - kind of the definition of "passive aggressive". That usually comes across as pretty personal, and doesn't end well.
Be mature about it. Discuss it out of game, and find a solution out of game as well. It is okay for the DM to say, "that isn't going to work in this game" - that's part of the DM's job.