I agree with your doc. I would be concerned too.
60 is hypoglycemic. Just because you felt fine doesn’t mean it wasn’t dangerous to be there. Different people have different thresholds where low blood sugar starts to be a big problem.
Look up guconeogenesis and alcohol if you want to understand what’s going on here and why fasting + keto + alcohol can make your blood sugar drop like this. The most concerning thing is the interference with gluconeogenesis can extend to processing regular carbs and if it gets bad enough, eating carbs may not raise your blood sugar rapidly. T1 diabetics are often warned about this, but it can affect anyone.
There are no loopholes. You shouldn’t drink while fasted. On the other hand, drinking at the end of an eating window can be ok. I will drink a unit or two of scotch at the end of my eating window and it’s fine.