Former "She fell over!" Chanter here. Stopped participating in it because I felt it wasn't right to use 'she' as an insult, there's nothing wrong with being a 'she'. It implies that being a female somehow makes you lesser. It doesn't really insult the player that dived like a filthy cheater, it only really insults women for their gender being used as a derogatory term.
As for the 'There’s too much sadness in this world as we’ve witnessed this last week to be getting uptight about these kinds of things' comments, yeah a portion of the sadness in the world can be attributed to men thinking they're superior to women and jokes/comments that sympathize with this position. You're right, there is too much sadness in the world, so lets try make the Fever a happy place, for both ladies and gentlemen :)
If you don't think the word 'she' in the chant is supposed to cause offence, then surely it takes away nothing to use the word 'he' or 'cheat' right?
There is certainly too much "Im so offended" in this world.