If she was criticized for using the book to support her position, I could agree with you, but I honestly haven't seen that. Personally I think she used the book to obfuscate the point she made, and I think it is proper to call anyone on that sort of thing--male or female.
Again, I wish she had just defended her position openly and said this is what I believe and why, but most politicians don't like to do that (and she is one of that pack).
I do recall how some gave Obama high marks for looking to Lincoln when he mentioned the book, but I was not one. Personally, I think the book glossed over some of the more prickly points of Abe, making him into a saint rather than the human being (flaws and all) that he was, but that is for another thread. Suffice it to say, in the instant situation that some parts of the book and film did show how Hillary's position could be used to positive ends, which is pretty much what her original quote you posted said.
And as for your citing the "double standard", I do not doubt that some have heaped criticism on Hillary because of her gender, but I have not been one of them. When I think she's right I will speak out; ditto when I think she is wrong. Criticism of a woman does not automatically trigger a double standard on the part of a critic, although some immediately choose to allege that.
ETA: This is a transcript of her remarks from Politico; I cannot state it is definitely a true transcript, but it correlates with my memory of what I heard:
As I recall, that was something I said about Abraham Lincoln. It was a master class watching Abraham Lincoln getting Congress to approve the Thirteenth Amendment. I was making the point that yes, it is hard to get Congress to do what you’re trying to do.
As I read that, she was not saying that she was not her position, but that it was Lincoln's position and she was discussing him and the movie 9and her position is that it is hard to work with Congress to get something through it). But anyone who wants can draw their own conclusions.