It appears that "JWT Token" service is incompatible with the Jetpack plugin that relies on the rest_authentication_errors to return true. AAM overrides it with false value to halt the nonce check during the RESTful API call for authentication.

This implementation has to be rewritten to be compatible with other plugins and for more information refer to https://wordpress.org/support/topic/jetpack-and-rest-api/