Well, I was just watching it one day and thinking 'yeah, I suppose you could see the scene in that way', etc. etc., not really taking it that seriously because c'mon, it was the 60s. I've seen some of the Batman TV series from that era and it's ridiculously camp but I'm not going to take it anywhere near seriously as a kind of covert gay thing because most people just didn't think in that way back then! It was cheesy, that's all there is to it. However, there was this quote from Gene Roddenberry (from an interview in Shatner's biography 'Where No Man...') that she talks about in the second episode that changed my mind:
"Interviewer: There's a great deal of writing in the Star Trek movement which compares the relationship between Alexander and Hephaestion to the relationship between Kirk and Spock- focusing on the closeness of the friendship, the feeling that they would die for one another..."
GR: "Yes, there's certainly some of that- certainly with love overtones. Deep love. The only difference being, the Greek ideal - we never suggested in the series - physical love between the two. But it's the- we certainly had the feeling that the affection was sufficient for that, if that were the particular style of the 23rd century."
Make of that what you will. The last sentence of that quote convinced me there was something else going on behind the characters.