I don't know about Car-x since we don't have them in my area, but any time I have trouble with getting out of a shop that was inspection only, I say I have to wait until payday, schedule the appointment to have the work done...say next week and then as soon as I leave, I call and "remember" I have a doctor's appt. on that day and have to cancel.
You have to remember it is the person's job who is doing the inspection to try to get you to have the work done.
Same thing with "look at a new car" shops...you have to have a ready excuse to get out if they are pushy. I have to go to work in 1/2 hour usually works. After all, they want you to have a job to pay for whatever you are "buying".
Terry9297