As an attempt to keep blog-spam under control, I require anyone commenting to leave a name and email address. I don’t care if they are real or valid – it just helps fend off the bots.
I don’t require you to be logged in to anything in order to post comments. However, it turns out that WordPress do (I host this on wordpress.com). If you try to comment using an email address associated with a WordPress.com account, and you aren’t logged in to that, then WordPress will ask you to log in.
This is not something I can turn off, unfortunately – part of the price of a hosted solution. 😦
If you see this, the easiest thing to do is use a fake email address. Add something like ‘-nologin’ to the end of you username (e.g. ‘joe-nologin@example.org’) – I can trim that off later when approving comments if you ask.
Software is too expensive to build cheaply.... 
If your client is not providing you with a detailed brief, I would suggest asking more questions.