Update, later in 2015
Well I'm resurrecting this thread because the answers still seem to be conflicting.
I booked a $300 United ticket on the Ultimate Rewards site a few weeks ago using about 24,000 points.
I just looked at my receipt on United.com and it says "ineligible" for PQDs.
Furious, I emailed United and they confirmed it was an ineligible fare.
... is going on? How can some Ultimate Rewards tickets work for PQDs and some not?