GitHub could not control what lies other websites tell. They can have a button saying “Sign in with GitHub”but totally not signing in with GitHub.
That said GitHub should have banned that website for lying and abusing instead of OP.
That said GitHub should have banned that website for lying and abusing instead of OP.
It makes a possibly dodgy website look more secure and legit by using a well known provider like Github for the login process.
In addition, it potentially exposes data from that well known provider, which is often sensitive data, as in the case of Github.