Overselling these days is definitely an issue.
One time I was a few minutes later at the ticket counter (28 minutes, say), it's a connection to ORD for an international flight (for the same reason I could not do OLCI). I as a 1K begged the ticket counter agent, that I only had carry-on, with a BP, and going through the elite line, there is no problem to reach the gate in 20 minutes or less. She was nice and did call (gate? control?) but told me no. It turned out that the flight was oversold. Instead of having one more PAX to DB, they of course like to stick with the rule.
Another time from the same station, I took a later flight to ORD for a domestic connection. The connection time in ORD was only 15 minutes. The flight was on time, and I got to the connection gate before the gate was closed. But the GA said no. Again that was oversold and they put another PAX into my seat. But I guess since I was a 1K, she produced a ticket and sent me to an AA flight leaving within an hour (UA's own next flight would be another 3 hours).