The FBI specifically has had expanded Congressional authority for like 10 years to operate extraterritorially on cyber matters

FBI agents will show up physically in any country and request cooperation from local municipal police (maybe) to seize electronic property as well as affect arrests in a way compliant with both jurisdictions. Given that private key crypto seizure is consequence free and irrevocable, if the FBI had access to the memory at a foreign data center they could have just taken it without worrying about local procedural nuances.

Using crypto the proper way already shield against this, because you have to assume that you can't trust your own security or the data center operators, let alone the state. The server should only have the Master Public Key[1] for giving a one-time use address and rotating down the index in one of the address trees immediately after any input is received (rotate to a new account upon receipt of funds, new accounts are from an infinite tree of arrays at each node). The mnemonic for the master public key would have been generated offline and never on any device. Moving the funds, whenever one feels like it, can be signed offline and physically handed to a node that will append the signed transaction to the blockchain.

[1]Bitcoin Improvement Protocols - BIP 44 (2014), BIP 39 (2013), BIP 32 (2012)

but anyway I'm leaning towards it being a private key on Coinbase that they got a warrant to check for, and it was correct, and they seized those assets