"No request new password" partially fails with "index.php?q=user/"

I still don't know if this problem comes from something I did wrong or not, but following my post in the "post-installation forum" (here) the developer wants to open the issue here.

A closer look at the behaviors of my test and production sites shows that both are doing the same thing. I'm using the latest version of the "no request new password" module with Drupal 5.10. It works normally if you log it at index.php, but here is what happens when you log in to "?q=user/"

Case 1: index.php?q=user/

"Request new password" tab appears. Mouseover produces an index line, not a hand, but you can still click the link. When you do, you get the "Username or e-mail address" form and the "E-mail new password" button. But even if you submit a valid e-mail address, you get this kind of error:

"Sorry, me@mysite.com is not recognized as a username or an email address."

So the module is working. It's just that you get this problem if you try logging in this way.

Case 2: index.php?q=user/1

In this case, you get the username/password form and login button without the "request new password" tab like you are supposed to, except that -- at least for me -- the display looks like this at first:

Access denied
_______thorized to access this page.

User login

Then if you refresh the page, it becomes normal:

Access denied
You are not authorized to access this page.
User login

Although I don't know if it matters, let me mention that I am using the FrontPage module to display the login form. Please let me know if you need more information.