To be honest, I wouldn't worry about it. As long as the signal is strong enough, you won't have any issues. I have RG59 running to my HDTV. Since the signal is all digital (just like DirecTV) you won't lose any PQ as a result of the RG59. I had DirecTV using the same runs as well, before switching to FiOS and have notice no issues. The only thing you would have to worry about is if there is a decent amount of intereferance where the lines are running - in that case, you could get stuff like pixellation and the like, but if you don't have that issue today with DirecTV, you really shouldn't with FiOS either (no, they're not totally analogous, but I would imagine that you would be ok).
Also, if the signals are strong enough around the house, the installer will just by default leave what you have. In that case, having him rerun the wires will cost you. If the signals AREN'T strong enough, then they'll rerun the cable anyway.
One last thing to consider - the ONT produces a very hot TV signal. So hot, in fact, that in many houses they have to actually attenuate it - they had to put an attenuator on one of my STBs. A really strong signal reduces the liklihood that you'll have any issues with picture breakups. Personally I wouldn't worry about it.