I remember somewhere hearing that William Shatner said that as he had no best friends, he drew on his feelings of being a spouse/lover/husband in how he fashioned his reactions to Spock. So it doesn't seem odd to me that people react to that. Look at what Spock says to Kirk in Star Trek V, when they tease the audience that Kirk is about to hug (or maybe even kiss Spock): "Please, Captain. Not in front of the Klingons." In the novelization, Kirk hugs Spock anyway (though they cut away in the film).
None of this means that I think they are physically lovers (I don't), but I agree that their relationship is flirtatious, romantic, caring, and deep and complex. I don't know what to call it, but t'hy'la makes sense.