A collaboration would work -- TMC wouldn't have to run it -- all I'd need is a subdomain on teslamotorsclub.com pointing to my server in order to access the vBulletin userid cookie and authenticate people that way (like tracker.teslamotorsclub.com) . But if I ran TMC, I probably wouldn't allow it.
The signup on EV-FW.com is already simple and nearly painless, and over 700 people have already signed up (over 140 new people since V7 was released), I don't think having it on a TMC domain to run it would significantly change overall participation.
Not knowing what percentage of the active TMC membership already participates I don't know for sure if it would significantly increase or not but in my experience it should. In any case your right about passing this token outside of TMC's domain to your servers. I wouldn't allow it if I were them either, they would have to host it which is likely a resource problem.