The user is then requested to confirm the encryption operation. So a "downgrade" could happen in two ways. The client selects nip04 without the user's instructions, and the signer does not properly guard or notify the user that the message to be encrypted is using nip04. Still not really an attack I don't think, since no "sessions" exist in DMs there shouldn't be any way a remote user gets to cause a client to change algorithms.
To answer directly, the client app chooses, makes a remote procedure call with the desired algorithm, user confirms, message is encrypted, returned, signed (another rpc round-trip), then written to relays.
The signer application is ALWAYS authoritative, if it chooses to.