They state that the seed phrase undergoes encryption and is divided into three shreds. These shreds are then directly sent to the three custodians from the Ledger device itself. When a recovery is requested, these encrypted parts are sent back to the new or old hardware device and decrypted back in the recovery seed. Nowhere does it mention that the shreds must pass through any Ledger server for encryption or decryption during recovery.
This means all shreds pass through your computer, and through Ledger Live. If Ledger Live gets compromised, your seed can get compromised. The whole point of a hardware wallet
used to be that your security doesn't depend on the security of the computer you're using.