If they have multiple accounts with the same email address, they need to actually request a password by using the Login Name. Otherwise there is no way to tell what account they need the password for.

Example:

account1: [email protected]
account2: [email protected]

If I request a password for [email protected] there is no way to know if I am requesting a password for account1 or account2. So I need to use the login name instead.