I am part way through reading the tribunal findings and I think you have misunderstood the trust's position and have also glossed over the fact that even the tribunal judges diplomatically referenced the claimants credibility deficit.
If you have read the document, including the legal principles at the beginning then it is apparent that there was no legal benefit to the Trust in trying to prove the claimant a liar. Not disputing the claimants allegations of transphobic abuse (specifically the two notes in the locker and the overheard conversation in the changing room) is not evidence that this actually happened. The Trust simply had to prove that they had done everything possible to prevent other staff discriminating against the claimant which they were easily able to do. Attempting to prove the claimant was lying would not have added to their defence at all.
The claimant stated that they destroyed the first abusive note they received, which seems somewhat implausible given their behaviour both before and after employment, so there was no tangible evidence that an abusive note had even been left. There was no corroborating evidence for the overheard conversation despite other colleagues being in the changing room at the same time and one of them helpfully supplying a list of everyone else who was present at the time the alleged conversation took place. The only tangible evidence provided was an abusive message written on a sanpro disposal bag but as no handwriting analysis was ever undertaken we cannot rule out that the claimant wrote it. A thorough investigation of all incidents was undertaken, the claimants account of events was inconsistent which was acknowledged by the tribunal judge.
The only thing we know for sure is that the claimant made allegations which could not be verified and there was no legal benefit to the Trust disputing the claimants account.