For folks with a paid, valid, normal fare tickets DL will not deny boarding until everyone is on the plane and those with seat assignments are usually not considered for IDB. That they decided to not not board you before boarding began indicates there was something non-standard with your ticket. Maybe AS did not issue it properly and rather than fix it DL decided to not fix it to further oversell the flight. Maybe the inter-airline tickets don’t have standard ticket properties and can be revoked by the alternate airline. Maybe it was something else. That the AS representative did not get upset by DL’s decision indicates that DL was within their rights to deny you boarding for some reason.