I think that you will have to report it as RIDDOR, given that is what the employee has claimed. However, your accident investigation should "find" what you found out and should be officially recorded. This way, if anyone did ever want to look into you can explain that due to the information you had from the employee at the time it appeared to be RIDDOR incident, however on investigation you found this to be the reality (this would include presenting it to the HSE if ever asked). I would then be looking at disciplinary for the employee for potentially "bringing the company into disrepute" - but that's a chat to be had with HR.

You can report your skepticism on the RIDDOR report as in "employee claims he fell at work, although this was not witnessed and followed a nasty fall he had at home two days earlier". Clearly if he did fall at work and at home then he might actually have something wrong with him so I would also advise a visit to occupational health at the very least as two falls in two days would be of major concern to me, even if you do think he is faking it.