MLB Rule Clarification: Runner Out on Interference After Batter's Strikeout

Question
In a previous question from Tom on 6/14/06 regarding dropped third strike with one out and bases loaded, I understand the dead ball and the b/r called out and for interference and the runners at first and second returning to their bases, but why is the runner on third called out?  

Answer
Hi Jim,

By rule if a offensive player already out causes interference the runner closest to home is also called out.  

In this case the batter was out on strikes and not entitled to try for 1st base because it was occupied w/ less than 2 outs.  They caused a play to happen on an already out player (the batter running to 1st).  The penalty is the runner closest to home is also called out.

Mark