Perhaps the problem here is more about terminology than about real functionality. The default route that is advertised by the ABR into the stub area gives the OSPF routers within the stub area a direction in which to forward packets whose destination is external to OSPF.
Perhaps it may help to think of it in this way: the External LSAs that are not flooded into the stub area represent destinations that are external to OSPF. The OSPF routers within the stub area will have LSAs that advertise all of the destinations that are within OSPF so they can accurately forward traffic to any destination that is within OSPF. But these routers within the stub area do not have LSAs for external destinations. So the ABR sends an LSA advertisement that gives the routers within the stub area an entry that they can use to forward to the external destinations.
HTH
Rick
HTH
Rick