I mostly agree with you.

> Those both seem pretty obvious, but put the two of them together and it means people can lose their jobs or not be hired for stuff they tweet. How do you resolve that?

If the employer happened to see it, then yes I think that's well within rights. But I think having some random stranger see something and actively campaign against the employee to their employer is a little bit different. It's not illegal, nor should it be, but there are plenty of things that are legal but still not good behavior. I would consider this under that umbrella.

OK, it's bad behavior. Now what? That means nothing.