PIR chooses and supervises the contractor that runs the TLD. I don't know if maybe, once upon a time, PIR ran the TLD itself, and then decided to contract it out.
It's not an unreasonable thing to contract out. Afilias runs multiple TLDs, and there are many operational things that would have a cost benefit from sharing; for example, running the anycast network of authoritative servers in as many points of presence as possible --- each PoP requires capital investment and time investment to setup and run, but servicing additional load may be possible at a much smaller marginal cost.