I have wondered if Jane may have helped Katherine and some part of her thought she was sticking it to Henry a bit. He really destroyed her life and she had to see him all the time, see him replace her family, and watch as he was giddy about his young wife while she had her family ripped from her. She should have been wiser counsel and a cooler head, it wasn't as if she hadn't lived in the shark tank that was court life. Maybe she played the long game and figured Henry got what was coming to him.