I doubt its a random check.

I wonder if there's a clone out there (not saying this car - this one might be the original)?

There's some sort of document that has all the details of the car on it - I seem to remember it's called a V5 - issued by the DVLA I think.

But we know there are circumstances where the details of the car and those on the DVLA issued V5 can differ. Obvious examples are clones, cut and shut jobs and jiggery pokery with write offs. DVLA would be derelict if they failed to have systems in place to deal with such possibilities. Another poster introduces possibility of vehicle having come off a personal plate (though nothing in OP suggests this). When we transferred a plate from retention onto our first Citroen Berlingo we had to take the car to the Local Office to be examined before the transfer paperwork was issued.

Following closure of the LVLO network examination is no longer required but some changes are selected for further examination either in form requested here or at an authorised MoT testing station.

Four weeks isn't that long if correspondence is going back and forth. Simple checks will probably be much quicker but if the pictures disclose need for further investigation.

They may do it because operating process requires it in a certain number of cases but idea that they'd single out someone at random 'because they can' is highly improbable.

OTOH if someone's attitude suggests there might be something afoot.....

I had to do this a few years ago before the current RFL system. It didn't take long and everything was ok with my car. But I think there was a reason for the check rather than it being random, maybe connected to a possible clone.