Most backup/observation cameras can be powered from one of the high-mounted rear marker lights adjacent to the camera's mounting location. Of course, that means that for the camera to be operable, the TT needs to be plugged into the TV and the TV's parking lights need to be on (not on "Auto").
IMHO, it seems excessive that a 4x-5x increase in labor cost would be needed to run a wire from the light to the camera location. To me, that may indicate:
- they think they need to run a wire from a new circuit on the electrical panel or the battery;
- they are trying to enhance their revenue;
- they are not familiar with the simplicity of the install;
- they don't want to take-on the job.
If any of the above four items are true, it's time to look elsewhere. Get another reputable outfit to give you a quote, since you now know that power needs to be run.