I saw that show. Great underwater videos. There is a German researcher that has said for many years that U-166 was sunk because she never returned to port.
There was never any doubt that it was sunk. The navy credited a Coast Guard PBY two days later that did attack something, about 100 miles away. The U-166 never radioed back to Kiel after the attack by Claudius (strong evidence favoring his claim). The U-166 was the only u-boat lost in the Gulf of Mexico, and was lost at the time of Claudius’ attack and in the place where he attacked.
By the way, the U-166 had four times the displacement of the PC-566, 1120 - (sf) vs. 280 Tons, and much heavier surface armament. If, instead of diving, the U-166 had turned into the her and surfaced, he could have sunk her by ramming or in an artillery dual. (The PC wasn’t worth a torpedo.) The German skipper seeing a “warship” closing on him in his periscope probably just wanted to get out as fast as possible. He may have been distracted by watching the Robert E. Lee sink in his periscope, and not seen the PC-566 until it was almost upon him and panicked.
The surmise by Ballard and his crew was that a depth charge exploding on the deck of the U-166 my have detonated one its torpedoes, and the rest of torpedoes in that forward chamber were set off by the first torpedo. Far too much damage for a depth charge.
http://www.uboat.net/allies/warships/class/463.html
http://uboat.net/types/ixc.htm