Calculated Measure to get only most current from one dimension on snapshot fact but keep other filters
You can try the following calculation:

Openings:=
CALCULATE( SUM( 'Requisition Counts'[NumberofOpeningsQT] )
         , CALCULATETABLE( LASTNONBLANK( 'Requisition Counts'[SnapshotDateKEY] , 1 )
                         , ALL( 'Requisition Status' )
                         )
         )


The important part is in setting the correct filter context for the outer CALCULATE.

With CALCULATETABLE, we define the specific rows which we want the outer CALCULATE to consider: the last non-blank snapshot date for all requisitions (or for a specific requisition, considering the context of each requisition on a pivot table), regardless of any filters in the requisition status, which is achieved using the ALL function.

The measure doesn't work exactly as you want; you say that you would expect the total for Approved to be 2. Using the 2013-11059 requisition from the Power Pivot model as an example, since there is 1 Approved status in 2013-07-01 and another in 2013-07-02, it just considers the last status for the total, resulting in 1.