I went to the Wayback Machine and went to "teamfortress.com" from 1998, which has a page for TF2. The page mentions that "Team Fortress Software" was working with Valve to make TFII, which at the time would've been Valve's Team Fortress, not Brotherhood of Arms. The specific audio demo listed is also present on this page.
Valve's Team Fortress and Brotherhood of Arms are pretty much the exact same game in all honesty, a lot of the same ideas got carried over, like the news ticker idea. There's a screenshot on the "Valve TF" page that shows a HUD with what looks to be a news ticker on the bottom, just without text.
They're two separate eras of development on the same exact idea for a game. Regardless, the audio demo would be more fitting for Valve's TF rather than TF2BOA.
