The idea that you can't form a connection with a team without being physically close is asinine. And hypocritical coming from you as well. How did you decide to root for the Hotspurs? Even if you go for the closest that would be either Swansea or Southampton. If you go by coverage it would have to be United, Chelsea or Arsenal.
Honestly as long as someone roots for the same team and watches them, who cares? Why does it matter to you why someone chose a certain team?
I don't know that I would really call myself a Spurs fan, I have zero Spurs gear, have never been to a match, and my life is not affected any way whether they win or lose. I do like to see them do well, but I really wouldn't be in the position to brag to people about being a Spurs fan.