I can't speak for Delta, but no, that's not standard practice.
Should you encounter a similar situation in future, ask to speak to Delta's CRO immediately. Every airline is required to have a CRO on duty during normal operations:
(a) Each carrier providing scheduled
service shall establish and implement a
complaint resolution mechanism, including
designating one or more complaints resolution
official(s) (CRO) to be available at each
airport which the carrier serves.
(1) The carrier shall make a CRO available
to any person who complains of alleged
violations of this part during all times the
carrier is operating at the airport.
(3) Each CRO shall be thoroughly familiar
with the requirements of this part and the
carrier’s procedures with respect to
passengers with a disability.
(4) Each CRO shall have the authority to
make dispositive resolution of complaints on
behalf of the carrier.
(There's more if you want to read the whole thing:
http://airconsumer.ost.dot.gov/rules/382short.pdf)