MCT is simply a carrier's willingness to accept the risk of a misconnect. UA isn't willing to accept the risk of a 20-minute connection at IAH, thus it's not a legal connection.

Domestic bags simply go on the next flight. If your bag made it onto the earlier flight, all the better.

Same thing for passengers. Had you made it to the earlier departure gate, had the flight not closed and had there been space (and you had no checked luggage), if there was time to reticket, you would have been boarded. But, had you not made the flight, it would not have been a misconnect.