Just, no

And I want to express my admiration for those who have been supporting Rebecca Tuvel as a person throughout the past week.  I want to apologize to her personally for any pain I caused by signing the open letter requesting retraction, especially given that I was a member of her dissertation committee.  I did not sign the letter lightly, and I do not consider the call for retraction a personal attack.

Just, no. This is why I should give up the Internet completely.  Yes, there is a person there, a person you attacked personally.  She won't apologize for signing the letter, but for "any pain I caused." The typical non-apology apology.  If you really apologize you have to say that what you did was wrong and that you shouldn't have done it, not just hedge your language endlessly.