Origin:

The "two base theory" or "god base theory" as many call it, originates from RoF movie where it was hinted that goku's base form probably rivals Super Saiyan god. However no explicit claim was made about that. Now, in DB Super, which essentially rewrote the movies, Goku said something like "I am the super saiyan with the power of Super Saiyan god" when he turns SSB. Hence many people assume that he had the power of SSG in base already. The fact that Akira Toriyama once claimed that Goku absorbed the power of SSG further supports this assumption.
However, when in U6 tournament, everyone is able to give base goku a hard time, people can't handle U6 characters being SSG level. So, there is now a theory that Goku can only use "SSG level power" in base when he uses his white aura.
The "theory":

According to this theory, sometimes, Goku uses a base which is on or above SSG lvl and sometimes he uses a base which is only slightly stronger than his BoG arc self.