You have got it spot on Herbie, old bean!!
It is simply not possible to escape one`s Statutory responsibility. It cannot be transferred,or ignored, or delegated or whatever term one chooses to use.
The contract for the sale of the vehicle is between the buyer and the Trader (the seller). The seller provides the vehicle and the buyer provides the consideration ((agreed price). A 3rd party warranty is wholly irrelevant, superfluous, a red herring, but is often offered by the seller to confuse, mislead, hoodwink, the buyer.
OK Geoff ?