Does it matter where Buddha was born? Why, yes it does matter.
If it didn't, why would you think both countries are adamant about his birth claims? Lumbini has a huge potential to become a pilgrimage destination for millions of Budhists. This directly translates to tourism and possibly billions of revenues.

Sure, if we start fighting in the name if Buddha, then that pilgrimage dream will never be realized, but don't tell me it doesn't matter. I just won't keep making fuss about it every time a no name celebrity opens his/her mouth about this issue.