It wasn't mistaken identity, or even a stab in the back. That said, it was a bit similar as Mill Sr unwittingly acted as a pathfinder, blazing a trail. To put it another way, I don't think Ed would have been on the radar were it not for his internationally famous brother. People voted for Ed, thinking in some way they would get Dave too. Ed on his todd, I don't think he'd have got it.
That said, it's like Ed was a megastar compared to the Labour candidates this time round.
Don't really see how it is that women have got a bum deal on this personally, some people seem to be implying that a woman should get the job just cos she's a woman, and it's their turn. Liz Kendall? Never heard of her before, she's the Blairite version of Ed. Up for it, keen, but no proof she can actually deliver. For all that, Burnham only ever has this look on his face like he's been taken by surprise. Cooper? Again, aside from the refugee quote, I can't see how she has said anything distinctive.
If you were cynical you could say that Labour gets a load of cash from lots of new members, so boosting the coffers, then it can ditch Corbyn when they are nicely in the black!