That's really wonderful -- though as others have said, I think you totally pass, too.
I find hospital staff to be really caring human beings. I was admitted to the hospital earlier this year and had to stay for a few days. I don't pass, heck I haven't even had laser done on my face yet, and I decided not to bother trying or bringing it up because I wanted a smooth hospital stay. Yet somehow the nurses found out I was trans (I've had a few years of hormones and have very long hair, so I do look a bit odd and they prodded me about it), and afterwards they insisted on using female terms, pronouns, and my preferred name that they got out of me.
The nurses were really sincere and encouraging about it and definitely took the initiative all on their own -- they even got really upset with the doctors for rooming me with a male, and moved him elsewhere. They loved talking to me about it (I told them it was okay and they wouldn't offend me) and really loved my voice. Only one really religious nurse was kind of questioning me about it, but she was still respectful enough, and another one got annoyed with her and said she needed to read more. I quickly befriended one nurse who talked to me a ton, and she said that if I were her daughter, she would have done everything in her power to be sure I wouldn't be struggling with my issue. That same nurse saw me at work about a month ago and was extremely nice to me, and said she missed me and was really happy to see me again.
I was really sad when I had to leave. I can completely relate to the feeling of safety and how much pain I was able to ignore because everyone was so wonderful to me. I'm really glad that you had an awesome experience, too, and I hope you get well very soon!