I think that despite your obvious and unvarying good intentions, it probably was an inappropriate question to ask of a third party.
I had been – for over a year! – in a similar situation until fairly recently. A fairly close social acquaintance (friend of a friend sort of thing) had developed brain cancer. And I knew that from conversations “around me” about him (things one picks up on without being nosy or trying to investigate, but if you’re as quiet as I usually am, and if you read friends’ postings on Facebook and other social media, then you learn things) – but neither he nor his girlfriend had specifically told me. So I was in kind of an awkward spot there, too. I did not know how common the knowledge was about his condition, so I couldn’t commiserate or express sympathy “because everyone knows”, and their social activities were cut down considerably, naturally, so I just didn’t see him any more. And I didn’t want to ask any of our mutual friends – those who were letting nuggets slip in various conversations and messages – so I just kept quiet and picked up that he wasn’t doing so well.
It was an awful place to be. (No, I’m not comparing “how awful it was for me” vs. “how awful it was for him”, because I know better than that, but it was still… uncomfortable.)
He made some temporary recovery this summer, so I did go on some outings with him and his girlfriend, and we had this specific conversation a few weeks ago. He had wondered why he never heard from me, and I told him straight that I didn’t want to pry, didn’t feel justified in asking if he didn’t want to tell me, and hadn’t been included in any notifications or updates, so I thought that he had wanted it that way, and just accepted it. He was relieved to hear that there was no rift between us. And I’m relieved that we had that conversation.
And fuck it anyway… he died a couple of weeks ago.
Still, I would do the same today.