Certain comment settings result in un-usable comment form

I searched through the open bugs but didn't see this particular problem.

The Problem:
I would like anonymous (non-account users) to submit comments. So, on "Administer -> Comments -> Configure -> Posting Settings" I have the following option marked:

* Anonymous posters must leave their contact information

Then, on "Administer -> Access Control -> Comment Module" I have the following options checked under comments:

<code>
                                                    anonymous user    authenticated user
access comments	                                         X                     X
	
administer comments	      
	
post comments	                                         X                     X
	
post comments without approval                                                 X

However, when I visit the site without my user cookies (e.g. with another browser, or after logging out), the comment form looks (almost) fine, but the code underneath is jumbled. For example, it should have the "Name," "Email," "Homepage," and "Comment" form fields available, but all is shown is "E-mail," "Homepage," and "Comments." There are two problems here:

1. The "Name" field is no longer displayed
2. The HTML underneath the "E-mail" form field is incorrect. See code below:

Here, you can see how even though the "E-mail" label/text is displayed, the form/text field next to it is actually for the "Name" information:

<code>
<div><div class="form-item">
 <label for="edit-name">E-mail:</label><span class="form-required">*</span><br />
 <input type="text" maxlength="64" class="form-text required" name="edit[name]" id="edit-name"  size="30" value=""  />
 <div class="description">The content of this field is kept private and will not be shown publicly.</div>

If anyone tries to submit a comment with this mangled form in place, then they're given an error that the email address hasn't been filled in.

If I change the "Access Control" settings to allow anonymous comments without approval, then the form shows up correctly. So, it's only under this certain circumstance that this problem shows up.

You can see this for yourself here: http://brilliantcorners.org/comment/reply/49, where if you try and submit an anonymous comment.