What is a "Partial Matching Index"?
I spoke to people much smarter than I and we will be documenting this soon™.

The actual definition of this, in the interim is:


  PartialMatchingIndexCount reflects the number of references that could
  be checked using index seeks, but the index key does not cover all the
  columns being checked. For example, the corresponding
  ForeignKeyReferenceCheck elements contain both a Seek Predicates and a
  Predicate element.


In addition:


  If this number is greater than 0, there is a potential performance issue, in case the partial matches result in large numbers of rows.