While there was some minor damage to the recovered Hunley structure such as one of the glass ports being broken, leading to the speculation that it may have been shot out during the attack, the amount of damage was not such as could not have been handled by mearly surfacing and abandoning ship if necessary. It is thought that that damage may have been caused by a WW II depth charge attack in the area against a German U-boat.
Remember that the Hunley did surface and signal a successful mission with the Blue lantern after the attack. Meaning that they could have abandoned ship at that time if any damage was serious enough to have been life threatening. It is at present thought that the crew dies due to exhaustion fighting the currents trying to get back into Charleston Harbor that night. That being the reason that the Hunley was found farther out to sea than the U.S.S. Houstonic wreck site.
Being unable to return to harbor before daylight that they may have simply settled to the bottom as they had practised, to wait for the tide to change and/or darkness to reenter the Harbor and fell asleep and died of lack of oxygen.
The fact that the C.S.S. Hunley did not or could not return from its mission may be what lead that "documentary" to the determination that the Hunley was not the "United States" first "Successful Submarine". After all it was A Confederate States submarine and therefore a foriegn powers submarine.