I think sperating K/S from its history is of course impossible, but I think seeing it in the context of the fact that it had never been explicitely said that it's NOT true does say a lot.
Of course they never kissed on screen, that's not up for debate. But lots of their interactions are coded in a way that if one of them were female, nobody would deny the potential off-screen-romantic relationship.
One of the important quotes from Roddenberry is in the petition you quoted above. That essentially says that if in their time homosexuality is accepted, then they'd be together.
Then he made up T'hy'la, which is a made up word created especiall to describe Spock and Kirk and he includes lover in the definition. In-universe it's of course possible to say that not all possible definitions apply, but on a meta level?
The fact that K/S has never been explicetely denied can of course be written off as fanservice, but in this case it comes from the shows creator and I do think that letting the interpretation exist as a validone over decades means that it shouldn't simply be written off.
I do recognize that in this case I have to give validity to the popular image as Kirk as the ladies man that exists in pop-culture, but I'd argue that "straight-goggles" are pretty powerful for (especially male) pop-culture and that this bias has to be taken into account.
This is a collection of K/S links:http://community.livejournal.com/kirkspock/172321.html
It's of course possible to argue that all this is written by K/S fans that come with their own bias and slash goggles, but I honestly think that many of the facts can't be denied if one sees them without the assumption that the characters are OF COURSE!! stright.
(One male character in a 60's show starts talking about how he's ashamed for his feelings for another male character and while he calls it friendship it's framed in two discussions about romantic love?)http://community.livejournal.com/tos_rewatch/6033.html