Are you sure if the other payment method doesn't have any condition?, such as; "minimum amount condition or buyer group" or is there is any country restriction for this payment method? IF there is a country restriction, then that option won't be available until the user is logged in, because it is only way to when the system get the country info of the user.
Provide me your joomla admin account to This email address is being protected from spambots. You need JavaScript enabled to view it. and let me check that payment method's parameters, then i can figure out why it doesn't show up.
Flexible Support Team