I may help a bit here.
The biggest case here is security. The most important thing is the EU law which says (185/2010) that if on board of plane there is no person with boarding card assigned to the baggage checked in (notice that the main case is not the person but the boarding pass on board), such baggage needs to be offloaded. So even if persons check in ok, but they would mix their boarding cards in gate before boarding and board the wrong A/C, this is not a security issue, no law has been broken. Apart from that no ID checks must be performed in EU during boarding....but the Air Operator procedures may be more strict. Which AO was here?