Is none better than some?

On the weekend I received a somewhat unusual request, concerning tournament byes. A player was considering entering the ACT Championships this weekend, but was going to miss a round, as he had another commitment. No problems, I replied, you can get a half point bye for that round. He thought for a moment and then asked if he could instead get a zero point bye. His argument was that he was more interested in playing competitive games than his total score, and a half point bye might give him a harder opponent than he would have received.
I thought about it for a while, and in the end said "Maybe". While I am inclined to say yes, I will probably think about it a little more, as there may be some side effects that I should take into account (especially if he gives someone else an easier or harder pairing than they might normally get).
Of course he was the player who was due a naturally occurring bye he would have no choice but to take the point, but the rulings on half point byes are not as clear cut. It is up to the organiser/arbiter to decide if they are available, but whether they must be awarded for every eligible game is not clear.