I don't agree with the boxing comparison. A professional featherweight boxer, while no match for a heavy weight, is nonetheless highly skilled and proficient. A 1300 player either has serious and significant defects, or is a child who is on his or her way up. In either case, the 2700 player has such skill that the only measure of interest is whether the 1300 can last 30 moves.
As a 1500 player in three simuls against a mere 2500 player, I beat the odds with a single draw. That was the only game that lasted more than 30 moves. That was a decade ago.

It's been a while since I posted on this thread. Had a change of thinking so here goes my input.
to me it's like yes it can happen, on the scoresheet.
1. "Can" is a permissive word.
2. If a 1300 beats a 2700 is it still a game of chess, or is it a game of who had a heart attack at the board and therefore forfeited the game, last (with all these crazy reasons for how it could happen, does the concept of "game" ("a form of play or sport, especially a competitive one played according to rules and decided by skill, strength, or luck." -Google) still apply?)?
Does the concept of "chess game" as a game of skill, still apply? hmmm...sort of. Chances are though that, were it to occur, the 2700 was willfully throwing the game (in which the "game" is not one, really), the 1300 was actually much stronger than his/her rating showed (in which case, the "1300" rating is deceptive).
This has probably been brought up, but this site (http://www.bobnewell.net/cgi/elop.pl) says that 2700 vs. 1300 winning probability is: 0.99968387220237 . haha. So the 1300 can draw or win 1 in 3162 games against a 2700. Personally I think that's not realistic. The 1300's chances are, in reality much worse.