I went back to the link in the OP and noted that there were also several readers who apparently objected to a picture of a snake on her site, saying they were phobic. Is that equivalent to the pregnant woman's objection?
I think if the pregnant lady, or, for that matter the snake-o-phobes, sent in an email requesting the pictures be removed, that is snowflakey, no matter how nicely it is worded. Not rude to ask, perhaps, but entitled.
If it was mentioned in passing and PW inferred a request, then I'm not sure. (Clearly PW feels there has been a request to have certain pictures removed, or else she wouldn't be apologizing for not removing them.) In that case I suppose it would go from snowflakey to passive-aggressive if their intent was to get PW to take down the photo but they just didn't say it outright.
I would actually liken this to attempting to change the parameters of someone else's invitation. "Yes, we'll come to the ice cream party, but we have to ask that no one serve dairy products, because I'm lactose intolerant." This is, "I want to read your blog about food, but have to ask (however directly) that pictures of food that make me sick not be published until I feel better." A blog is someone's personal forum, and I think it's like insisting you be allowed to set the tone for hospitality offered in someone else's home.