I've heard this argument when it comes to female politicians. They can't act the same way as their male counterparts without being accused of bitchiness.
I think there is definitely some truth in that.
On the other hand, what Powergirl is describing here in a male counterpart is someone like Guy Gardener. And he is a polarizing figure so I don't know about him getting away with stuff unchallenged.
Although, he definitely does get away with more shennanigans that a female counterpart would be able to.
Could you imagine Powergirl mooning the JSA?