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.