The lower left pistol in the picture below is a "Government" Mark II model :
Along with every government contract, at least all those I've dealt with in the past, are provide with specific attributes that must be included with the finished product. Certifications are also require and presented when the contract parts are completed.
From all the Ruger reference material I have, there's nothing that mentions "special barrels", but I sure am open to reading where that information came from. What one, main specification involved, was that the chamber be "roller-burnished" to a specific diameter, roundness and hardness. the sights had to be targeted and set specifically also. Tom Ruger and another engineer designed equipment to do just that, thus the provided target accompanying all Ruger Mark II Government pistols when sold new.
Those models involved with the government contract were indeed marked U.S. on the receiver ring.