They are perfect by definition of perfect play (neglecting 50-moves rule). Definition of perfect play is what beck15 explained few posts ago. Here is nothing to agree or disagree about that.
That definition only works if one side has a winning position. It doesn't work for equal positions where neither side is winning by force.
It does, because in an equal position, they are both attacking (for shortest victory), as well as defending (for longest resistance). An inaccurate move from either side can spell their downfall. And by definition, an inaccurate move is not perfect.
If neither side has a won position, you've got the task of working out which of the selection of non-losing moves is preferable. This isn't so easy. "The shortest victory" only makes sense if the player can force victory, i.e. has a won position already.
The only way I can think of is if the 1300 player was a high rated player(strong in his/her game) before playing on the chess.com website and played the 2700 player. there are many strong players in the world that do not play in Official tournaments, like taking their show on the road so to speak, or such circles. that is why an "Unrated" new player can be a dangerous opponent. but I say if you have nothing to lose and everything to gain by trying... by all means TRY !!!