Yes, the air is certainly dryer when you get above timberline. Plus, of course, you are sun-exposed more, and that will drain water out of you as well.
OTOH, once your body has adapted to high altitudes, it can operate there quite nicely on only a moderate amount of fluid.
I left Whitney Portal one time and consumed only 8 ounces of Gatorade getting to the summit.
Also, your water usage will be unpredictable if you are using Diamox for altitude. I suspect that few backpackers use it for JMT altitudes, but I know some that sure do. With Diamox, your water intake and urine output tends to run high for 2-3 days until your body reaches a new water balance point, and then it gets normal.
I was on a very high mountain trip one time, and the rest of the group was taking Diamox, but not me. Their water intake got all squirrelly for a few days, and they thought that they were getting sick. Then a water crisis hit us, and there was insufficient water for cooking or drinking. I don't think that it phased me. Everybody is different.
–B.G.–