As I understand things from talking with a TSA suit who was asking people what they thought of PRE while they were collecting their things.
The airlines role beyond creating the barcode with the encoded yes/no is to simply select pax who the airline believes would benefit from the program.
From there if the pax agrees for the extra DATA to be shared with TSA, TSA determines if the pax is eligible for PRE.
I asked why the PRE line had like 5 people while the Elite Line had tons or people in it, he indicated to me that at first TSA had a quota per shift/day (he was not specific) at each airport of PRE eligable people and if things progress without major issues with the program those quotas will be raised over time.
Dan