if you buy and fit a 4″ shim but only insert the post 3″ its not the required insertion.
Minimum insertion as marked on a post is the required amount to avoid the seatpost from flexing too much and snapping.
You should follow frame manufacturers advice for seatpost insertion, you seem confused, that you mention
I prove them that I inserted almost 4″
then say it was 5″
Would either depth reached below the triangle for the seatpost?
When I changed my trek to a yeti, my existing reverb post wouldn’t fit, 31.6 down to 30.9. I just bought a new one and used the packaging to make existing post look better on ebay, only lost £25 – seems like it’d have been the best option.