Charles Helliwell's Answer:
It is unusual for an employee to take such a direct and bold stance with a manager without any obvious rhyme or reason to do so. You must first be absolutely confident that you have not unwittingly precipitated such an action; either directly or indirectly. Unknowing cause for such behaviour on your behalf, as a manager, can be no excuse, when you finally unravell the circumstances which lead to it.
Having said that, this employee's actions are wholly inappropriate and totally reprehensible. Your immediate reaction will be to defend yourself, your authority and your credibility, which I suspect will be the actions expected and anticipated by the perpretator.
Consequently, do not follow this route of predictability, as anyone duplicitious enough to have instigated this, will have already planned and predicted their next course of action, based on their anticipation of yours.
Instead, go on the offensive, rather than the defensive. Take him to one side and tell him that if he feels so strongly, you will happily accompany him to meetings, which you will arrange, with both your Manager and the HR Manager, when you will expect him to formalise his grievance and provide evidence to support his claims.
This will be the last thing he will expect you to do, and it will either force him to withdraw and apologise or proceed and provide proof to back up and substantiate his claims. Either way, you will have regained the initiative in this matter and will be in control of what happens next, as opposed to controlled by the circumstances of a situation, which were not of your making in the first place.
Should he choose to proceed, you will, of course, have first briefed your Manager and the HR Manager on the circumstances surrounding this grievance, so that they are both fully aware that this matter may be brought in front of them. Be prepared that both of them, may well be reluctant and somewhat detached and neutral participants in any process which follows, as they will see it as nothing more than a shallow and superficial slur.
However, also be aware that in spite of any reservations they may have privately, they may not decline your request, because of the serious nature of the allegations being levelled at you, and the implications that these could have on you and them respectively.
But before you embark on this somewhat unconventional and perhaps even radical approach, you must be as sure as you can, that you really are 'whiter than white' in this matter. This solution is as close to 100% guaranteed as you can get; however it's something of a 'kill-or-cure' option and is not for the faint-hearted.
Most managers do prefer and tend to opt for the easier choice of a compliant compromise solution and hope that their mischevious employee finds better sport elsewhere in the company sooner or later.