Very true in my experience.
Another piece of data for those having issues:
I put in the galloway precision trigger which is just a piece of plastic that changes the angle of the trigger pull, lowering the amount of travel, which resulted in even better shooting for me.
As others have said, I...
I haven't shot the LCP II but from video reviews understand there are some differences. They are similar size and weight though.
I imagine if you are accurate with one you have a good chance of being accurate with the other despite minor design improvements of the max.
Disclaimer: I'm sure some people had legitimate issues with their Max but for those who the problem seems to never go away, this might help:
I saw several posts about the LCP max shooting low and it usually goes like this:
1. Person says the gun shoots way off they have been shooting for...