" They've said that when they issue a warranty, if the building control checks aren't done by them then they instead issue the warranty based purely on their own guidelines."
It is incredibly rare (read: unprecedented, in my 35 years in the industry) to find a warranty by the NHBC where they didn't also undertake the building control. It just wouldn't make any sense. The exception is in Scotland and Northern Ireland, where different systems apply and the NHBC are not allowed to take on the Building Control function.
There is a single application form (known as a SNIN - Site Notification and Initial Notice) to the NHBC that covers both building control and warranty registration. The 'site notification' is the NHBC warranty part and the 'initial notice' is the formal notice that the NHBC is instructed to tell the Local Authority that they, not the Local Authority, will be handling the building control... the whole NHBC system is therefore joined at the hip, so to speak.
It does have a separate tick-box to say whether you want them to undertake building control or not, but I've never known anyone who would use them for warranty but not BC, and once you've filled in that form, the rest of the process is entirely seamless between the two sides, so far as the developer/builder is concerned.
I don't know how far you'd get, but you might try asking the NHBC to provide a copy of the SNIN for the site, which might give additional clues.
If you are 100% certain that neither the NHBC nor the Local Authority handled the building control, then unless you can establish who did deal with it, don't walk away - run.