It is hard to tell at what point does the door start to bend, is it at the knot or somewhere else.  If it is at the knot then have at them with full force as it is a manufacturing defect.  If it starts to warp elsewhere then you should still pursue them but it would be a little more difficult as they have already stated a position.

If their issue is humidity, lack there of, you might want to consider placing a humidifier in the room with the stove to offset the dryness.

I think the truth lies in the grain.  The grain in those boards and the elongated knots mean it is almost assuredly plain sawn wood - the cheapest/easiest kind to make and also the most dimensionally unstable.  I would think any woodworker worth his salt would use quarter sawn or rift sawn wood - at least for the door frame on a $5K door.  This method costs a bit more because there is more waste, but the wood is substantially more stable.  The “tiger stripe” grain of the plain sawn wood might be more visually appealing - and perfectly fine to use for the door panels, but the frame needs to be stable.

This page explains it pretty well:
http://westcoastlands.net/SawmillCuttingMethods.html

The warp starts at the lowest knot just above the bolt and gets worse as it passes through the upper knot.
I agree it should be quater sawn, especially on a door of this cost.

Well that is how the Co. makes their money.  Use cheaper wood in the hopes that most will not warp, as most users do not put it through the exteremes that a wood burner may do.  If there is a failure blame it on the wood stove as that is the exception to what they typically see, and not on their poor wood choice.

I would fight tooth and nail to get it replaced or fixed.

Appears they are backing off on the wood stove cause I showed them that at a wood stove temp of almost 600 only raised the temp of the door to about 80 and that the rel humidity in the house was 30% plus the stile is now starting to delaminate and the knots are more open. Looks like I might get a new door.