Stu, I really don't know the answer to your question. If you're staying at Red Rock, of course, use of the spa comes with the room. Actually, it's included in the resort fee, but if you're comped, you don't pay that. Are you being comped at Texas? If so, you won't pay their resort fee, either, but if you were paying it, it would be less than the fee at RR, which is considered a "resort property."
My suggestion would be to call Red Rock's spa and ask them their policy on this, instead of relying on people here who are doing nothing but speculating. Let us know what you find out.