Where is this section? The only similar statement I can find is where they define someone as "hired" which is when the pilot begins training. However, hired isn't what they are committed to. They are committed to making offers.

I think this section pretty clearly defines US Airways' offer commitment:

4.
e. The following conditions apply to US Airways’ Offer Commitment in any given year:
i. The Offer Commitment will be fulfilled based on offers made to Piedmont pilots for New
Pilot Positions, regardless of whether the offer(s) is/are accepted, or whether the
Piedmont pilot fails to appear or delays appearance as scheduled for an assigned new
class hire date, or fails training. For example, if US Airways has an Offer Commitment for
27 Piedmont pilots, and US Airways makes offers to 27 Piedmont pilots, but only 15 of
those Piedmont pilots accept the offer, and three of those fail training, US Airways will
have fulfilled its Offer Commitment for that calendar year.