For blogs in which the owner has elected to allow anonymous comments (there seem to be many of those and I've intended to allow that on my new blog), I think the following idea will help avoid the confusion. On the comment form, the email input box is captioned "Email [lotsofspace] (Address never made public)". For the cases of anonymous comment election, I think it should say "Email (optional) [lotsofspace] (Address never made public)". This would help clarify to readers that the option to post anonymously exists and is done by omitting the email address in the form.
Apparently, there remain difficulties in some browsers keeping login states in situations where users would be reading blogs instead of writing them, and commenting. I know Firefox has this issue. When 2 or more tabs are open on the same site, and a child tab logs in, the parent tab doesn't always get the cookies.
This all means that the only way to avoid the login prompt is to not give an email at all. But people have not always done that in the past, it seems. They will need to change behavior a bit and this can give the hint to them. Hopefully that section of code emitting that string has access to the flag that indicates anonymous comments are OK.