I have seen the date of May 9, 1944 given also. In addition, I have read some commentary that it actually happened in the Gulf of Venice which was why they knew right away that it was a German ship.
I have not read an actual pilot account. Just stories based on the account. I have also seen credit for the sinking listed somewhere on the web chronicling the Tuskagee Airmen's accomplishments.
It's possible that they got the area where the attack took place wrong. That's not an uncommon error. It's also possible that the Germans listed it as a bomb casualty since it was an explosion would have done the ship in. One does not need to actually see the bomb falling onto a ship to conclude that a bomb struck it if there is a terrific explosion in the midst of an air attack. It is assumed. Only the attacker knows for sure whether they used bombs.
I'm not sure why you are saying that they didn't know which plane they were flying. In mid 44, they were using P-47's.
I can't imagine that it was dreamed up. Such a claim would have been verified and these were black pilots. The 40's were an era of pretty severe racism. Making up incredible accomplishments for blacks wouldn't have been the order of the day!