Believe it or not, I think I actually did this.
I'm pretty sure I was Tanya at the time (only because we were going through all the characters to see their fatalitites), but I don't remember who my friend was. Anyway, somehow it seemed that my fatality and his Hara Kiri actually synchronized, and the camera completely wigged out. When the screen went dark, I thought I had done my fatality, and he thought he had done his Hara Kiri.
It's tough to say what really happened, because like I said, the camera wigged out and it never really focused in on either fighter, it just kept jumping all around. I think the end result was that I (the victor) had a leg bone stuck in my neck, which doesn't make any amount of sense, but that's what it looked like to me.
It was obviously a really freak thing that's not supposed to happen, but I don't know what to tell you, because I can't explain it any other way.
I agree with sim, it does seem like it'd pretty impossible, but I still can't explain what happened. It's also possible that it wasn't a tie, and that either my fatality or his Hara Kiri just happened to glitch out at that moment.
Sorry I can't help any more, but if you ask me, given what I saw, I think a "tie" is possible.