I flew MSY-IAH-SAT today. Arrived at IAH about 2:45, was booked on the Express flight to SAT at 4:10.

Ran from the depths of terminal C to E where the 3:05 SAT departure had not finished boarding. PDA site showed availability for standby.

First I was told by the gate agent there "was no room" and then she asked if I had checked baggage. I did have baggage but indicated it did not matter if it made the flight or not. The gate agent told me she was not allowed to put me on the earlier flight if I had checked baggage. Is this true?

I waited around for another 10 minutes and overhead the red coat telling the gate agent not to wait for three connecting passengers as she didn't want to take the delay. Based on the PDA site, I can only assume that meant the flight left with at least 4 open seats as I did not see them clear any other standbys.

The insult to injury was the backtrack to terminal B.

Should I have been allowed on the flight?

Because you checked in bags, no - they can't do it. Security reasons. (Bags must fly with paxs because it could be bomb or whatever.)

It is quite possible to be on a flight that does not have your bags on it. Otherwise there would never be lost bags. That said, generally passengers are not allowed to separate themselves from their bags, which is what the OP was trying to do.