Thats true. It's imperative that the company knows your MEC/NC speaks for you. So when they bring back a TA that the pilot group votes down, it becomes quickly apparent to the company that the pilots in the room really weren't speaking for you. So now when your NC tells the company, if you can give us X, we can find a way to make Y work, tye company may not believe them, and will be super hesitant to give them X. Or if the NC tells the company, we can't get to a deal unless we have Z + 3 because the pilots won't take anything less, the company may just laugh and say no, because they no longer believe what the NC is telling them.
Successful negotiations are mostly about trust between the two parties. A failed TA (when the parties are actually working together towards a solution) wrecks that trust. Putting the same people back in the room will generally not lead to successful outcomes unless the required fixes are very small and simple.