I think the Hutchinson/Henson/Leaf/Wright/Stoerner/Testaverde days are plenty of proof that he won't draft a QB high even when there is a glaring need.
He drafted Carter in the 2nd round of 2001, the offseason following Aikman's departure. The Cowboys didn't have a 1st rounder that year.
Carter had issues and was released after the 2004 draft, but had been the Cowboys' starter in the 2003 playoffs. In the 2004 draft, Jones had thought Parcells had rejuvenated Carter's career and was focused on improving other areas of the team-- a playoff team.
1989-2000: Aikman starting, hurt first game of 2000
2001: Drafted Carter
2002-2003: Not ready to give up on Carter, but took a chance on Hutchinson with no pick
2003: Believed Carter or Hutchinson was the guy, and with Leftwich, Boller, Grossman, Ragone, et al the QB class after Palmer was worse.
2004- Believed Carter was a playoff QB, though took a chance on Henson
Carter was released in August 2004.
So we're really talking about 2005, and that year Parcells demanded the rebuilding of the defensive front. I think Payton and Parcells had faith in Romo and Bledsoe for the long and short term, and it's been legitimately all-Romo since.