Please provide specific date(s) & flight number(s).
Also, were you actually able to complete your award booking(s) or were you just told that there was availability?
As to the first point, I'll have to go back through and look when I'm at a computer with KVS (not the one I'm at right now). I do remember that it wasn't just one day, or one flight number. It was the same two flights (IB only has two flights daily to TLV), and for a number of dates from late May to early June, BA and KVS only agreed about 80% of the time.
I didn't complete the award booking because I'm still holding out for better dates. However, I was on the phone with BA and they claim they would have been able to book, and online I could go all the way up through the final confirmation screen. They were also showing plenty of availability (more than 4 seats on each flight). Maybe this is a problem with QF more than it is with IB/BA?