Originally Posted by AuAAdvantage
Actually, I was more concerned about being delayed by them and
missing the "next plane back to the U.S.", i.e. mine.

I have never been hassled by BRU customs, and I flew there twice a month for the last six months of 2004. (This was for work, and not MR's). The only possible hassle is a line/queue at customs. Around 7am, a UA flight arrives and so do a few flights from Africa (?). Around 8am, you have AA flights from JFK and ORD, a CO flight from EWR, and a DL flight from ATL. So, it can get a bit crowded.
After getting your passport stamped, keep walking straight, and then head left to the exit - passing all of the baggage carousels. Once out of that area, take the escalator up one level to check-in level.
If you're arriving on a flight from a Schengen country, then disregard the above info. In this case there will be no passport check. You will just have to walk (a mighty long walk) from terminal A to terminal B and go through security. Terminal A is Schengen, and Terminal B is all others (UA, AA, CO, DL, BA, BD, etc.).