Actually, it does affect your faction status. Steal enough [censored] from a faction, and you lose status with them. I had gotten to vilified against Ceasar simply by robbing the camp while I was there on his invitation, without attacking anyone.
I think you only gain infamy if someone sees you stealing.
The problem is that the Owned rules are applied inconsistently. Sometimes things that should be 'owned' are okay to take (stuff in Doc Mitchell's house), while other times stuff out in the wastes is marked as owned even though it seems abandoned.
Sometimes the owned tag doesn't seem to work properly, too. I was in the Novac gas station gathering crafting supplies. The stuff wasn't showing red, but suddenly I got a message about being vilified by Novac? After the message, suddenly all the stuff was showing in red! I reloaded to a recent autosave and went back, and this time the stuff was showing as owned. By keeping hidden, I stole it all without ruining my reputation in Novac.