You're confusing the Army with the Navy.
Navy personnel are familiarized with the M14 due to the large numbers kept in ships' armories and because it sees use (with an adapter) as a tool to launch ropes from one ship to another. Recruits in the US Army are issued an M16A4 in basic training. There is no issuing of the M14 in basic as soldiers who are issued an M14 are issued it at the unit level and are familiarized on it there. (I could be wrong on this point, could someone who was issued an M14 in the Army clarify?)
The M14 is currently issued in small numbers to fill a designated marksman role. Like any other designated marksman rifle, its purpose is to extend the effective range of the individual squad by an additional 100-300 meters. It is not meant to replace any 5.56 weapon, it was simply the best fit for the required role. 5.56 out of an M16 series weapon will kill a person just as well as any other weapons system. It all depends on the situation and the skill of the operator. The US military chooses which weapon systems to adopt for a good reason. As such, there was no "dusting off" of old rifles as M14s have been used as a supplement to the standard fireteam ever since they were replaced as the standard infantry rifle in 1966.
I wish there wasn't so much weapon/caliber fanboyism on the internet because these misconceptions and rumors about one rifle or caliber being SO superior to another, (X round will bounce around in your skull, Y round will kill you just by passing by) are started and spread so easily due to uninformed individuals reciting things they heard second or third-hand.