No this is not true, however, there is one scenario where it only “seems” to be true but it really isn’t.
First, you need Link installed and active as that is the only way a link between as user and a Connections entry can be made.
The one scenario where this would only appear to be true is if a user logged in with Link active and “their” entry in Connections didn’t have a matching email address. If you would change the email address either in the entry or in the user a link still would not happen because Link will only check once and then mark that user so they will not be checked again. The reason is because Links are persistent, meaning, after a link has been made, it will still exist even if email addresses are changed. Why is this, simply because people frequently change email addresses so you would want that link broken just because they updated their entry and not their user profile. The other reason is security, help prevent the hijacking of Connections entries so unauthorized changes can not be made.
Hope that makes sense and helps!