It seems pretty obvious to me that some people don't understand the the fundemental difference between a defensive midfielder and a deep-lying playmaker. A deep lying playmaker doesn't go charging about breaking up play, he covers defensively but his main function is to start up attacks.
He needs great passing ability not great tackling ability.The Germans have used players in this position for years , with Beckenbaur the first (that I am aware of) playing there later in his career.(he eventually dropped even further back and became a sweeper). Basically its similar to a sweeper but instead of playing behind the back four they play in front of it, reading the game, covering defensively and building when in possession.
Sammer (East Germany) and Matteous late in his career also took on this role. While not brilliant tacklers and losing their pace they had the experience and passing ability to link things up at the back while sweeping passes out to set up quick counters.Modern day exponents would be Pirlo ( who again started out much further forward) and Alonso.
They are not true defensive midfielders as their main job defensively is cover, not breaking up attacks in the way that a true defensive midfielder like Mascherano, Hamman, or Sissoko would, but sitting centrally deep, usually with the better and more aggressive tackler beside them (Gattuso for Milan and Masch/Hamman/ Sissoko at Liverpool) to do the chasing, harrying and generally making a nuisance of themselves.
While pace is always an asset, this role enables a player lacking pace or whose pace has dwindle withthe years to still exert a huge influence on the game, without exposing their lack of recovery when attacks break down.
In a nutshell their main function is being the focus of starting attacks with their defensive duties secondary.
Hope this helps.