First off, there's no statutory or common law offence of urinating in public so there can only be an offence under a local bylaw, which wouldn't apply within the bounds of a hospital unless covered by hospital bylaws issued by the Secretary of State under a Power.
Second, even if a bylaw did apply, there is no offence until and unless the action has been reported to the magistrates and they have found the individual guilty.
From the facts, this does not sound like a public place either: a public place is commonly taken as meaning any street, road or other place to which the public have, or is permitted to have access. This is a wide definition of a public place, which would include the lobby area of hospital, but not an area that the public is not permitted to access, even if visible.
Notwithstanding the foregoing, the evidence appears to be circumstantial, strongly so, but circumstantial nevertheless - probably enough weight under balance of probabilities for civil action, but not necessarily compelling in a criminal action, especially as the manager cannot actually evidence the act - simply the fact that the gardener was facing the shed. The gardener may assert that he was investigating what appeared to him to be evidence of someone urinating in the garden, which is a reasonable and plausible explanation. Similarly, there is no proof of his lying - only two versions of what was observed.
If the manager witnessed the alledged offence, rather than get a witness to verify the existence of a smelly puddle, why didn't he or she challenge the individual on the spot, in flagrante - I would expect a senior manager to have the strength of character to do that much. Instead, he/she seems to have dumped ownership onto HR - fairly typical in my experience.
All you have is the word of one person against another - you lack independent witnesses. For all we know, the manager might have a grudge against the gardener - there's no evidence of that, but there is almost as good a case as the rest of this for saying so. Nor is it appropriate to ask him if there are any medical or health issues which have a bearing: this is for three reasons (1) you have not not actually established he has behaved as alledged, (2) assuming he has, you are effectively asking him to incriminate himself by admitting to a contributary medical problem and (3) you have no justification for what could amount to an invasion of his right to privacy.
I chair appeals against misconduct and dismissal decisions for a very large employer and regularly have to uphold the appeals because of the weakness of the case against the employee and this would probably fall into that category. In short, there is no proof of gross misconduct, and no real case unless the gardner suddenly turns around and says "fair cop, guv". There is only an assertion, not substantiated with direct evidence and as a disciplinary panel chair I'd be well ticked off with any case brought to me on appeal on this basis.
Sensibly, all you can do is put the allegation to him as you have done . Take him at his word on this occassion, but with the caution that if there is a recurrance then adminsitrative action will be taken dependent on the circumstances at the time and, if he or anyone else should be caught behaving in this manner, it will be assumed to be gross misconduct unless there is strong mitigation.
In the meantime, tell the offended manager to get out there and challenge the gardener at the time instead of leaving it for others - I fear this is more reflective of his/her sensibilities than it is of a real desire to demontrate firm management and leadership.