In your opinion, and your opinion only.
Tbh, I personally don't think you've a clue what you're talking about.
Week in, week out I get people telling me I shouldn't have failed something, or I should have done this that or the other, and 100% of the time they are incorrect.
I introduce them to the testing manual (which is available online), which always clears things up.
Because they are responsible, obviously, they sold the car.
You can appeal the MOT decision if you like, but if the car has any faults etc, then your first port of call is with the dealer that sold it.
If you bought a toaster and it was faulty, would you contact the maker of the toaster or take it back to the shop you bought it from?
Actually, I can imagine you sat outside the Russell Hobbs factory, toaster in hand waiting for the factory to open so you can complain about a faulty heating element.
Give me strength.