It depends on how you define it.
Naturally, in a combat situation the Marines and Army are NOT going to be the "safest".
But overall safe regardless of war or peace.... Then the US Navy is actually the LEAST Safe, despite many opinions that they are the MOST safe.
"What was that?" you say. "You're joking!..."
Nope. The US Navy is the most dangerous of all the branches to serve in when you take into account the totality of the service and not just combat only.
What I mean by this is that to the average sailor, the dangers involved during peacetime operations are the same as during wartime. Whereas with Marines and Army, the level jumps from being higher to being lower than the Navy.
When the Army trains during peacetime. it's little more than a high stakes version of Laser tag. enforced camping trips. and marches. Not very dangerous at all though accidents happen from time to time.
When the Navy trains, the dangers are just as real as wartime.
While Army and Marine training "SIMULATES" warfare... Navy Training is the real deal... not simulated.
The dangers of working on the flight deck of an Aircraft carrier couldn't give a rat's behind whether the planes are taking off to drop live ordinance on some ISIS or Al Qaeda MF'ers... Or just taking a lap around the ship and landing again just for the flight practice.
Storms and the related hazard of being at sea could not care less if it is wartime or peacetime.
Simply being at sea is hazardous duty and Mother Nature will kill you dead in a heartbeat if you forget that.
IF the weather gets too bad for the Marines and Army... they just reschedule their exercises.
We don't have that luxury in the Navy (though we do try to avoid Typhoons/Hurricanes).
So while in immediate combat, the Army and Marines danger level is higher.... Anytime outside of direct combat, their level drops to below the danger level that is consistent throughout the navy at all times.
So overall... the Navy is the "Least Safe" generally speaking.
MOST safe belongs to the "Chair Force" {{Ahem}} I mean Air Force.
J/K...
All joking aside... other than Pilots, Aircrew, and certain specific other jobs... The Vast majority of Air Force personnel rarely see dangerous conditions. Though working around aircraft and live weapons on an airfield is dangerous, it is nothing compared to being on the constricted flight deck of a carrier at sea, in addition to the dangers inherent simply being at sea.