Hello,
I don't know if this helps but we've deleted the user's Mysite site collection from Central Administration, gave the user permissions to upload documents, but still prompted to log in; none of this helped us but may help you.
Our particular user is still being prompted to login with username and pswd but this just reprompts her each time. In our case, the user was just updateding their site with a new background theme when first login box occurred. Hope this helps!
Regards,
Larry