Even if the chargeback was wrongfully processed by the credit provider, that doesn't get Ryanair off the hook for EC261. I don't recall any set-off provisions in the Ryanair T&Cs that would allow the airline to collect any monies it claims are due from future purchases on ryanair.com or that would invalidate a newly purchased ticket.

The passengers were issued with a ticket by the airline, they had a valid reservation. Article 2 of EC261 provides the following definition of 'denied boarding':

"(j) "denied boarding" means a refusal to carry passengers on a flight, although they have presented themselves for boarding under the conditions laid down in Article 3(2), except where there are reasonable grounds to deny them boarding, such as reasons of health, safety or security, or inadequate travel documentation"

Article 3(2) provides that this provision shall apply "... on the condition that passengers ... (a) have a confirmed reservation on the flight concerned and, except in the case of cancellation referred to in Article 5, present themselves for check-in ..."

Where does the existence of an alleged debt get the airline out of that? I see the contractual position of the parties and the statutory protections of the passenger under EC261 as two very separate and distinct legal obligations.

If a passenger is denied boarding because of a chargeback on an unrelated reservation then the airline is exposed to liability under EC261, irrespective of whether or not the chargeback was illegitimately actioned in the first instance.