That's not quite true.
VIPs, global mods and admins can set/change their own custom titles, but everyone can display one (eg get one assigned to them by theymos).
An example for that would be Blazed, who's neither VIP nor involved with moderation, but holds the custom title "Casascius Addict".
Custom titles are also given when theymos does name changes, eg for BitcoinPenny (formerly CJBianco), who carries their old name as custom title "aka CJBianco".

tl;dr: Everyone can have a custom title, not everyone can set one for themselves.

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Hilarious' "Lamborghini Member" and mprep's "Diamond Member" is poking fun at the Copper Member rank that was introduced a while back.
As you can see, custom titles show at the same place as the "Copper Member" text when people are posting (not on a users profile).
I would assume rickbig's "I'm not a member" is meant in a similar way.