It does not seem to make much sense what you are saying because OAuth is already a form of authentication. So either you use OAuth or Basic authentication.
The OAuth class uses the HTTP client class which supports Basic authentication, but if you only need to make Basic authentication requests, you only need to use the HTTP client class directly.
phpclasses.org/httpclient
On the other hand, I suspect that you are doing something wrong when using OAuth and the server is falling back to Basic authentication.
Can you please tell what API are you trying to access that requires Basic authentication?