The following is taken directly from the tpwd website:

"You are allowed to quarter a deer or antelope in camp, but tagging and proof-of-sex requirements continue to apply until the wildlife resource reaches a final destination."

"Final Destination" for Pronghorn Antelope, Deer, and Turkey:
The permanent residence of the person who takes the antelope, deer, or turkey; the permanent residence of the person who receives the antelope, deer, or turkey or part of the antelope, deer, or turkey; or a cold storage or processing facility.

This sure seems to indicate that the processor should expect to receive proof of sex, a tag and a quartered deer as that would be the final destination if not processing yourself, but maybe the actual law is written to cover the OP's circumstance. I don't think I could fault Cinnamon Creek based on the above.

I had a situation back when they were Syracuse where I dropped my cape off at the taxidermist prior to taking my meat to be processed. The taxidermist insisted he needed the tag and gave me a wildlife resource doc. When I got to Syracuse, they indicated they needed my tag. I explained the situation, called the taxidermist and had him fax a copy over. Problem solved. Tag should have stayed with the carcass, not with the taxidermist btw.