On edit - I think the hostages intentionally crashing the plane may have been put out there in the early days and it stuck in my mind. Looking at websites about it now, I see accounts such as the following:

Worried that the passengers would soon break through to the cockpit, the hijackers made the decision to crash the plane before reaching their final destination. At 10:02 a.m. a voice was recorded saying, “Yes, put it in it, and pull it down.” The airplane then rolled onto its back and plowed into an empty field in Shanksville, Pennsylvania, at 580 miles per hour.

Another article linked to below shows I'm not the only one who remembers the early story:

Sasseville didn't end up intercepting Flight 93 because the passengers devised their own plan to take it down. The plane ultimately crashed in Shanksville, Pennsylvania, killing everyone on board. But those passengers averted a fourth attack.