No, Palin wasn't at fault for the Giffords shooting. It was standard Middle American misogyny:
"It was not just his appearance — the pale shaved head and eyebrows — that unnerved them. It was also the aggressive, often sexist things that he said, including asserting that women should not be allowed to hold positions of power or authority.
One individual with knowledge of the situation said Mr. Loughner once got into a dispute with a female branch employee after she told him that a request of his would violate bank policy. He brusquely challenged the woman, telling her that she should not have any power."
http://www.feministpeacenetwork.org/2011/01/17/loughner-didnt-think-women-should-hold-positions-of-authority-or-power/As for the NY Times, a complete joke publication that cheerleaded the Iraq war, and likes to pretend it's above the likes of Breitbart but
partners when them when it suits them.