Other than not having gone to the hospital with your friend there's nothing you could have done differently, Crispy, and in my book not supporting a friend in need of medical help is not an option.
It is a fact that many some of the most flawed individuals who walk this earth go into 'public service' and their 'uniform/status' blinds many to the man/woman behind the 'hero' persona they are able to present merely because of the work they do.
When he was full-on in the pub, putting his arm around you, behaving as if he'd known you for years, I suspect that warning bells were sounding; you were thinking wtf but you didn't feel able to call him on it because 'this man regularly sees things that would send someone else bonkers, he puts himself on the line for others and he deserves to able to let off steam in his off-duty hours'.
Maybe you were too busy 'rationalising' along the lines of 'okay so I don't like all this tactile stuff, but maybe this is just his way of sloughing off the 'horrors' that are part of his work and who am I to judge him for that? He's obviously a man's man, full of bonhomie, likes his extreme sports, and it's no skin off my nose to listen to him bore for England for a couple of hours in gratitude for the work he and others do rather than any attraction I feel towards him' to get your brain round the fact that this man was showing you who he is.
When he 'insisted' on walking you home, who would have foreseen the harm in that? If you'd keeled over in the street on any other occasion you'd be heaving a sigh of relief if he, a paramedic, came along and when he asked to use your toilet, how could you have refused?
Could you have said 'sorry, haven't got one' or 'sorry it's not working' and sent him off with his legs crossed? Who among us would have said 'no' or stood at our open front door until a 'hero' had relieved themselves? And what chance would we have stood if the the 'hero' dragged us in and shut the door?
And let's not forget this man wasn't some random you and lets not forget that this man wasn't some random you'd picked up from a bar/club or the internet. You'd seen in him his superman outfit and had every reasonable expectation that he'd be as well-mannered as Clark Kent in his off duty hours.
I can't see anything in the above for you to blame yourself for, can you?