How very confusing BAC3.
I would suggest contacting the Berkshire Archives which is located in Coley Avenue in Reading and asking them if they have the full admissions and discharge records for Broadmoor, particularly for the period you are interested in.
If they do then it might be worth asking them for a quote to look up the records you're interested in, as you know the admission date that would enable them to find the correct treatment file quickly which would show not only the reason for his admission but also why he was transferred to Rainhill Asylum if that was the case. I'd suggest treating the FindMyPast information with caution until you know for certain how long his stay at Broadmoor was.
I used the research facility at the Berkshire Archives earlier this year and they were very reasonable charge wise and didn't set a minimum time even if the look up would have taken them less time. I set out the background to my enquiry and it obviously intrigued the archivist who checked for me judging by her report. I'd suggest doing the same for your Thomas.
Unfortunately I've lost contact with the former Director of Security and Assistant Director of Nursing at Broadmoor otherwise I'd ask him to check their records for me.
Another thought occurs to me and that would be to get a copy of his death certificate, for £7 for a PDF copy from the GRO that might be a good spend and resolve some issues . I think that's the route I'd take. I was typing this when Ciderdrinker posted.
Let me know if you do find out he did in fact die at Broadmoor and I can send you a photo or two I have of the cemeteries there if you'd like that. If the Berks Archives do find his admission and medical records they should show which ward block he was accommodated in and I should be able to identify which one that was - they changed the names a few times - and identify that on readily available aerial photographs.
At one time Broadmoor had its own operating theatre and surgeons came from one or other of the nearby large hospitals to operate on patients when necessary. It also had a separate nursing ward(s) to treat patients with physical illnesses that couldn't be treated on their regular ward. If Thomas was discharged for physical illness reasons I would be quite surprised as Broadmoor being newly built would have been able to look after him as well if not better than other Asylums.