No. Emily's blue-check-mark Twitter bio is ALL about her professional activities, and 90%+ of her tweets are work-related, making it a de facto professional account. The fact that she drops an occasional personal tweet onto her clearly professional Twitter account does not transform it into a personal account. If your argument is that it is not unprofessional to post Tumblr-esque selfies and you're-so-hot DMs on a professional Twitter account, then we simply disagree. But if you are arguing that a Twitter account used by a paid sports writer almost entirely to disseminate material related to her work somehow escapes the designation of a "professional" or "work related" account, well, you're just wrong.
And for the record, Emily -- or any other person -- can post whatever she wants on her professional Twitter account so long as her employers are okay with it. But it's the internet, and people are free to react to it. If Hack-cosky decides to post Speedo shots of himself on his Twitter, would it be "over the line" for us to make fun of him for it?