we are both using different computers to access the form
a server can send the same page to multiple people at a time regardless of whether the user needs to login first.
when you visit can.com and view a news article, it is also being viewed at the same time by many other people.
this is no different from a form page.
now the key, is that when the form is submitted, you will want to collect information specific to the user who filed it in
when a user logs in, their is is saved to a session. when the form submits, you want to collect the session along with the form information.