The test Overeem failed was given to the ENTIRE card, not just himself (I think it was UFC 146 and it was after a press conference).
The only 3 fighters I can think of that ever had a random test in the UFC were Overeem, Carwin and Roy.
http://nbcsports.msnbc.com/id/24387162/
google and bing are majikal like this. imagine that; just enter a question, and out pops some answers!!!
BJ and Rory as well
I think they volunteered though, which is different.
I googled UFC random drug test, and pretty much only UFC 146 stuff came up and the UFC policy on it
EDIT: thanks for the link though, I didn't know that the AC had random drug tests for MMA back then
Roy and Carwin volunteered as well.
BJ and Rory still had to take tests at random points in time, so I'm pretty sure that constitutes as "random drug testing"
it probably wouldn't have been done if Sherk hadn't failed a test earlier in his career. and for whatever reason they decided to do both.
the real answer to your question, i think, is that for many states (cuz it's different in every state) the AC's require random testing for those who have ever failed.
Would they not have had to take the tests if they didn't volunteer? I thought the Roy Carwin was from the AC, but the BJ Rory one wasn't and BJ was offering to pay for the tests during their talk fest leading up to the fight.