Who quoted this? A coatings rep/supplier or the finisher your hiring?
So many variables here, so it is really impossible to say. If I were to give a wild guess I would probably estimate a minimum of around 2-3 gallons of clear to be on the safe side. This is getting into the territory where a 5 gallon pail might be more cost effective, or close enough in price. The particular product may also only be available in 5 gallon pails.
I also err way on the safe side with stain, especially when mixing custom colors since you really don't want to have go back and match what you have already applied. You never EVER want to have to do this if you can avoid it.
Bottom line is that it may very well be extra material, but I don't think that is an unreasonable figure, and there is probably a good reason for that.
If your the finisher, use your own judgement. If your hiring someone to do this, and picking apart their bid, cut them some slack here because they are using their judgement, and they probably have a good reason to spec this if they are reputable. You could simply ask for a clarification, and perhaps reiterate that the backs will not be finished.