We've had OUR airplanes in customer livery for many years. Some of them you might have seen (over Atlas' history) but not realized were actually Atlas airplanes include:

British Airways
China Airlines
Thai
Emirates
Alitalia
Scandinavian

In each case above, the airplanes were owned, registered, and operated by Atlas Air and pilots (and FE's on the 200s) on the Atlas Air seniority list.

Other customers that we fly for are ok with the Atlas livery and their cargo on our airplanes.

That includes using their traffic rights, landing slots, and even their callsigns...

For those of you that look down on such things, just take a look out of the window of any major (legacy) airline and you'll see a Regional Jet painted in the livery of the contracting carrier...but operated by someone else. It is no different for Atlas.