Low Oil Level Indicator?

[Best4x4xFAR]

Okay,

So we are still in the first couple weeks of new ownership of our '06 CPO X5. This weekend on startup (warm, had been driven only 30 minutes prior) I get a 'Stop Engine Oil Pressure' message that comes up, literally, just long enough to read it, then goes away. So we drive to our next destination (about 30 minutes, maybe 20 miles) and when I turn the engine off I get an 'Oil level low' message.

I happen to be right up the street from the selling dealer, so I drop by, and the message won't come up, but they take it over to service to look at it. Bring it back 15 minutes later, saying it was about a 1/2 quart low, they topped it off, and the remainder of the quart is in the back.

Just how sensitive is this low oil level indicator? I would think it would have to be a full quart or more low to get such messages. Of course my salesperson (who first tried to check the oil level by going through menus on the NAV system -- after a couple of minutes I couldn't stand it anymore and suggested he use the dip stick to check the oil level) says 'oh yes, it is very sensitive', but....

Note, the truck was parked on level ground in both instances, so I wouldn't expect any effect on oil level from outside factors. Should I be worried?