Looks like your right. The US has:
https://en.wikipedia.org/wiki/Sikorsky_CH-53E_Super_Stallion... as its near equivalent with a external payload of 36,000 lb. The Russian helicopter carries 8000lbs more at 44,000lb, though Wikipedia doesn't say if this is an external or internal payload.
Looks like a 40ft shipping container weights around 8000lbs empty, couldn't find a stat on full. It seems such an operation would be outside the capacity of these helicopters. Sure they could comfortably lift empty containers, but probably not full ones.
Russian Military has: https://en.wikipedia.org/wiki/Mil_Mi-26
That's the one they've used to rescue downed US helicopters :)