Correct.

I also mistakenly thought the cake baker was a sole proprietor. They are incorporated. I should have done a simple search before posting my original comment.

That said, I now mostly agree with the comment I was originally replying to.

> What does limited liability have to do with a corporation being owned by one person?

Correct, nothing. To clarify:

My position is that an entity enjoying limited liability (which in the US includes an LLC or corporation owned by a single person) has exchanged "rights" for indemnity and therefore can be compelled to - for example - bake a cake or not censor content hosted on their servers, but that a sole proprietor can do whatever they want re: refusing service or moderating content.