> Appointed by President Obama allegedly as a sort of "Olive Branch" to the Republicans.

It was an “olive branch” to Republicans in much the same sense as the British sovereign offering the leader of the party that has secured a majority the opportunity to form a government is an “olive branch” to that party; it is, through combination of law (limiting the number of members of one party, and mandating Senate confirmation before a nomination becomes an actual appointment) and established custom (as to how nominees that are not of the President’s party are chosen), a requirement that, if violated, would produce a major crisis.

It's not an olive branch. The President is required to appoint no more than 3 members of one (his own) party, and 5 total. The chair is then designated by the President.