One word, Purity when she was outed.
The "Unwritten Rules" are unwritten for a reason. Both sides play fast and loose when they can get away with it.
Sophia fed them bad intel. But yeah, things could have been done much better but given that they kidnapped Aster the moment Purity was outed and hid her away while Purity rampaged, it is not that much of a streach to think they planned something like this.
Edit: as for the purity case of PRT are idiots, this is not quite the same. that was a bad judgment call, and then everyone refused to back down, going from "If we have her baby, she will have to sit down and accept any demand we throw at her""IF I DON*T GET MY BABY NOW, EVERYTHING DIES" "she is making counter demands, but we can't negotiate with terrorist... didn't think this far."
Wasn't that Coil rather than the PRT?
A lot of PRT bullshit is Coil trying to discredit the Piggot, but it's not like the PRT is totally incompetent with every other agent belonging to Coil.
IIRC it wasn't even the PRT who took the baby away, though they had 'PRT' support/backup and it was done so fast it HAD to be pre-planned.