My read is that Bostrom had reason to believe that the email would come out either way, and then he elected to get out in front of the probable blowback.
As evidence, here is Émile Torres indicating that they were planning to write something about the email.
That said, it's not entirely clear whether Bostrom knew the email specifically was going to be written about or knew that someone was poking around in the extropian mailing list and then guessed that the email would come out as a result.
In any case, I think it's unlikely that he posted his apology for the email unprovoked.
It's a fair point that we should treat Alice and Chloe separately and that deanonymizing one need not imply that we should deanonymize the other.