A FlyerTalk Posting Legend
Join Date: Sep 2009
Location: Minneapolis: DL DM charter 2.3MM
Programs: A3*Gold, SPG Plat, HyattDiamond, MarriottPP, LHW exAccess, ICI, Raffles Amb, NW PE MM, TWA Gold MM
Posts: 100,417
I doubt that some technical problem with the check-in system at the gate would be an extraordinary circumstance under EC261. It's also very odd that such a problem apparently affected only one passenger, namely your daughter.
Whoever is responding from DL seems to be confusing the EC261 IDB rules with those of the DOT.