Each country sets their own laws, so it’s ultimately up to the destination country. When an ordinary citizen visits another country, they have to meet requirements for entry, but countries can negotiate any terms their government allows them to. So as long as the US government works out terms with the other country in aadvance, they can send anyone.

The US government does have an advantage other countries lack: we have military bases all over the world, including a lot of “shithole countries”. There are separate agreements negotiated over the use of that land, but I bet that the US can send whoever they want there without declaring to fhe local authorities who they are. Then the US can “conveniently” lose track of them and… poof! No more undesirables…