I think you're right.
The '81-'83 had the single row chain and it should be converted to the double row chain if it hasn't already. If not, it needs to be replaced every 30,000 miles.
The '84-'85 380 SL's came from the factory with the double row timing chain.
FWIW, in Europe they always used the double row timing chain starting in '81. Why the brilliant engineers at MB went with a single row in the U.S. is a mystery...
2001 E430, Bourdeaux Red, Oyster interior.
1973 280SE 4.5, 170,000 miles. 568 Signal Red, Black MB Tex. "The Red Baron".