The diet is meant to be moderation with plenty of veg etc, not the rich meals now everyone is eating in the south. In Spain, Portugal, Italy, I see everyone eating heaps of candy, way too much meat, no moderation etc. That's not the 'mediterranean diet' the way the term was meant. So yes, if you call fat + sugar the mediterranean diet, then it's a lie, but that's nonsense.
I have lived many years both in north and south Europe, and I can tell you that south is way, way, way healthier, with 5–15% consumption of ultra-processed products against 40-50% in the north.