Yes, I don’t see why the police could not have issued a NIP as soon as the report was made to them (or a least very soon afterwards and certainly so that it was served within 14 days).
The argument the police are using should not succeed. They had a report made immediately after the alleged offence occurred. They had no reason to doubt its reliability. They had no need of proof that the offence occurred to issue a NIP. They could have obtained the Registered Keeper’s details immediately. They had no reason to require footage and, in any case, there may not even have been any. What then? They don’t bother to pursue what, on the face of it, seems to be quite a serious transgression?
The police issue NIPs for reports of minor collisions with stationary vehicles in supermarket car parks. There is often no footage and all they have to go on is an allegation that one vehicle struck another.
It seems to me they have made a prize balls up.