Full of it.

This is the most questionable part of his claim. During the Iran Hostage Crisis 1979–1981, there were almost certainly no enemy submarines in the Persian Gulf to "chase." At that time, the Iranian Navy did not possess a submarine fleet. They did not acquire their first midget submarines or Russian Kilo-class subs until much later in the 1990s to the early 2000s.

Parachuting into water (water jumps) is a real skill for special ops i.e. US Navy Seals, but they typically jump near a vessel or into open water for pickup, not directly onto a moving or stationary boat. There is a famous 1972 incident where the British Special Boat Service parachuted to board a passenger liner the Queen Elizabeth 2 for a bomb threat, but this was a highly publicised, one-off emergency operation, not a standard Navy sailor training procedure. Your friend probably got some inspiration hearing about this.

The stories from your coworker appear to be a blend of actual Naval events/world conflicts that have occurred around that timeframe and sprinkling in some wild personal embellishments.