In the web a stateful protocol is based on having a temporary token that is exchanged between a browser and a server (via cookie header or URI rewriting) on every request. That token is usually created on the server end, and it is a piece of opaque data that has a certain time-to-live, and it has the sole purpose of identifying a specific web user agent. That is, the token is temporary, and becomes a STATE that the web server has to maintain on behalf of a client user agent during the duration of that conversation. Therefore, the communication using a token in this way is STATEFUL. And if the conversation between client and server is STATEFUL it is not RESTful.
The username/password (sent on the Authorization header) is usually persisted on the database with the intent of identifying a user. Sometimes the user could mean another application; however, the username/password is NEVER intended to identify a specific web client user agent. The conversation between a web agent and server based on using the username/password in the Authorization header (following the HTTP Basic Authorization) is STATELESS because the web server front-end is not creating or maintaining any STATE information whatsoever on behalf of a specific web client user agent. And based on my understanding of REST, the protocol states clearly that the conversation between clients and server should be STATELESS. Therefore, if we want to have a true RESTful service we should use username/password (Refer to RFC mentioned in my previous post) in the Authorization header for every single call, NOT a sension kind of token (e.g. Session tokens created in web servers, OAuth tokens created in authorization servers, and so on).
I understand that several called REST providers are using tokens like OAuth1 or OAuth2 accept-tokens to be be passed as "Authorization: Bearer " in HTTP headers. However, it appears to me that using those tokens for RESTful services would violate the true STATELESS meaning that REST embraces; because those tokens are temporary piece of data created/maintained on the server side to identify a specific web client user agent for the valid duration of a that web client/server conversation. Therefore, any service that is using those OAuth1/2 tokens should not be called REST if we want to stick to the TRUE meaning of a STATELESS protocol.
Rubens