Actually, yes. "Oversold" doesn't mean they will need volunteers or need to dole out vouchers. No-shows, misconnects, etc. Reminds me of a time I was in CVG waiting for a flight several years ago flying standby on some flight. The GA told me I had a good chance to get on. Then a couple minutes later he got on the PA and asked for volunteers. He wanted them "just in case" he needed them. It ended up he didn't need them and I got on the flight no problem.
Often "oversold" flights go out with empty seats.
I think if you wanted to take an earlier flight from the same city, you might have had a chance at the airline taking you up on your offer. But a different city requires a ticket reissue, so I can see why they said no.