Definition of a Deep Stall
I believe you are correct and the terminology they used was incorrect. What possibly is being described is sometimes called "mushing". Some aircraft are capable of having the airspeed bleed off until the elevator is all the way up - it then mushes with a high descent rate to the ground. 

I owned a Navion that would do this. If you slowly bleed the airspeed off and add full elevator it will end up with a 500-600fpm wallowing descent and severe buffeting (full aileron may be needed as the wings rock side to side). 

Several Piper aircraft are also similar such as the PA-28-140 Cherokee. The Cherokee is known to run out of stabulator during flares and can pancake onto the runway - no damage but an embarrassing hard thump. 

I have flown just about all the single engine and small twin engine Cessna's and none of them will do this. They have lots of elevator and are always capable of a nose dropping full stall.

Captain "Sully" Chesley Sullenberger reported he was aware the flight computer of the Airbus A320-214 did this (US Airways Flight 1549, "Miracle on the Hudson") and deliberately held the yoke all the way back and let the aircraft mush onto the Hudson River.