Claim: Andre Veilleux, a right wing from Montreal Rangers (LHJAA), was the first pick for the round one of the 1965 NHL Amateur Draft; followed by Andy Culligan, a forward from St. Michael's Buzzers (MetJHL).
Evidence: He was the first overall pick in the 1965 NHL Amateur Draft, picked by the New York Rangers, but he never played professional hockey. 
1st overall, 1965
New York Rangers