I wouldn't have thought the inspector could refuse to sign something off because you might make non compliant chances later. He might mention on a personal level that fire doors are provided for an extremely good reason, but I doubt his personal suspicion would come into it. Building control do have enforcement powers on non compliances for a year after the work is done, and if something is dangerous, the powers never expire. Although I'm guessing they're more used for people undermining their foundations or dangerous electrical installations.
The inspector will sign off whatever he sees on the day, if it's compliant on the day.
The issue is, fire door sets are controlled fittings and so should not be changed unless its to the same standard. Ok, fit another fire door, but then who is checking the installation? The ironmongery, the fittings, the strips, the manufacturer's guidance, and most importantly the gaps?
If there is a fire, and these doors don't perform then there will be questions as to who certified the installation, and if there is none as the doors were replaced, then probably no insurance cover is the very least that could happen. Potentially worse.
Fire doors are literally a hot topic ATM, and will be under intense scrutiny for years to come.
But yes, bottom line is do what you like in your own house as no one will know.
I'd be checking fire doors on a buyer's survey and confirming that they are the original ones as certified by the inspector, and not taking it for granted.