No they're not lying - it just takes a bit effort to find them (I know I tried for atleast half an hour).
Go to http://www.ea.com/
and log in (red button on top right) with your email address and password
the go to 'EA Support' (there's a link on the left hand side and one in the 'quicklinks')
Click on 'My Account' then enter your username and password, click login button - you may have to do this several times on different screens for it to work (it took me four attempts...)
'My Account' will then open - click on 'My Games' tab: It lists all
your EA Games with their registration codes.