Well, this is really simple. You will just need to issue a few commands on your terminal and you will be able to disable Recent Documents in Places.

All you need to do is create a .gtkrc-2.0 file in your home directory; edit the .gtkrc-2.0 file and add a line to the file. Once that is down just save and exit the changes made (:wq)

Steps

$touch ~/.gtkrc-2.0  /*Create this file in home directory*/
$vi ~/.gtkrc-2.0  /*Open it with vi or gedit, I used vi*/
gtk-recent-files-max-age=0  /*Add this line to the file and save and quit*/

Save and exit the file (:wq) and you successfully disable Recent Documents in Places.