The US Navy has been launching missiles from underwater platforms for over 50 years: http://www.spacedaily.com/reports/US_Navy_Marks_50th_Anniversary_Of_First_Submerged_Launch_Of_Fleet_Ballistic_Missile_999.html
The 'shopped video of a fighter aircraft "launching" from underwater is actually a video of a Polaris launch, with the missile replaced with a fighter.
http://www.spacedaily.com/reports/US_Navy_Marks_50th_Anniversary_Of_First_Submerged_Launch_Of_Fleet_Ballistic_Missile_999.html
The 'shopped video of a fighter aircraft "launching" from underwater is actually a video of a Polaris launch, with the missile replaced with a fighter.