I could believe modern factory farming, preservation, and mass-preparation techniques make meat much less healthy (than it used to be in our ancestral days), but a general "meat cooking brings carcinogens [to a level that matters, beyond plant cooking does]" sounds pretty unlikely too.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4191896/
https://www.sciencedirect.com/science/article/pii/S000291652...
The only diet studies are observational, and they are unreliable in all kinds of ways. The famous Blue Zones book has about the validity of Rich Dad Poor Dad or The Millionaire Next Door. But the book continues to sell, and at a macro level, its advice is not terrible, but it's also not "the only way."
Surprisingly (to me), there is some evidence that some people are genetically better disposed to eating a vegetarian diet than others.