This isn't about the permalink structure of WordPress; all you need to do is add a slash to the action attribute in the form
so instead of
<form action="verify.php" method="post">
do
<form action="/verify.php" method="post">
Note the slash before verify.php; that signals to the browser to post it at the root directory (blog.com/verify.php) instead of on top of the last directory.
(The permalink structure is only relevant to the extent that the lack of a file suffix confuses the browser into thinking got-a-question is a folder rather than a file, so it tries to stack on top of it.)