score:7
can she request a refund for being allowed boarding despite being inadmissible?
No. Eligibility for entry into the destination and any intermediate stops is solely and universally the responsibility of the traveller, and as such the airline carried out their contractual obligation to the traveller in transporting them to the destination and back again. The refusal of entry at the destination is not the responsibility of the airline.
Itβs true that airlines have an obligation under ICAO rules to the destination state (either ultimate destination or transit stops) to not present ineligible travellers, which is why they often check documentation and eligibility before travel begins, but this obligation does not extend from the airline to the traveller. Airlines can receive fines from states for each ineligible traveller they present where suitable checks have not been carried out, but this infers no responsibility to the traveller at all.
As such, no refund is due - the airline carried out their part of the contract without issue.