How likely is that, exactly? Was Aaron Rogers not at the top of our draft board when he slid and we passed on him?
We used our first pick on Quincy Carter in 2001.
You could make an argument for Byron Leftwich in 2003: he went two picks after we took Newman.
You could certainly argue for Rodgers in 2005; we passed on him twice.
Tim Tebow went one pick after Dez, but I don't think anyone but the Broncos had him as BPA.
Two QBs went in the three picks after Tyron, but the BPA was pretty clearly Tyron or Watt.
Tannehill went two picks after Claiborne...but we traded up for Claiborne, so we pretty clearly had him as BPA.
We passed on Manziel for Martin, thank God.
Apart from that, I can't find a draft where a QB went within 5-10 picks after Dallas, so yeah, I think it's likely that Dallas never thought a QB was BPA at their first pick, except for Carter, maybe Rodgers (where we certainly weren't alone), and possibly Leftwich.
I didn't look at the trades down, so there may have been times they had a QB at the top of their board but opted for the trade instead.