I struggled to get the mug back on the base. I blamed this vertical pin (yellow circle) which I think IS the locking pin and the reason the base doesn't twist off. Rather than cut it off, I just bent it flat against the mug and then put the mug back on.

I couldn't get the mug to twist back, but I had to lightly hammer it to get back together, and it seemed solid, so I just left it as is.