Is there a reason why UA would prefer to do involuntary denied boardings rather than ask for volunteers?

Here's why I ask -- my girlfriend was on a packed SFO->ORD flight today (on a 744), which was oversold. However, we never heard any announcements in the boarding area about asking for volunteers, so she got on. As the flight was nearing departure, I was standing around the podium watching things (I had already gotten bumped off my flight), and I heard one of the gate agents (she seemed to be the one in charge there) tell somebody something along the lines of, "I know you've got a confirmed reservation, but there aren't any more seats -- the flight is 100% full." When she was questioned about asking for volunteers, she said that they had already asked for them, both on the plane and off. (Later, when I was talking to my girlfriend on the phone, she said that she hadn't heard any such announcements on the plane). End result, the flight went off full, and 21 people (they announced the number) were denied boarding.

As I see it, there are three possibilities:
1. The gate agent was telling the truth, and we somehow missed all the announcements asking for volunteers (seems unlikely, especially since there was no sign up on the podium, which there had been for my flight, which wound up only needing 3 volunteers).

2. the gate agent came in late to the picture and was misinformed -- she thought a legitimate effort to get volunteers was made, when in fact it hadn't been.

3. the gate agent was lying, and they had decided from the start that they wouldn't really try to get volunteers.

Based on what I saw and what my girlfriend told me (which may be wrong), it seemed like number 3 was the case. Is there a reason why UA would prefer to just do involuntary denied boardings rather than looking for volunteers? It seems like, even if the costs are higher for VDB vs IDB's, the amount of goodwill lost would be more. There were a lot of _really_ angry people at that podium... (which made the gate agents' lives harder, so it's hard for me to see why they would prefer that, as well)

Dan