Your link is about death rates, not heart disease rates. Can you give me some graphs of heart disease rates over time with sources? There are plenty of studies which show that societies that eat more meat have higher rates of heart disease. I have yet to see a study showing the opposite which is why I said it's absurd.
I also read some more of the "articles" on that site you linked to and they were absurd on their face. Here is one example. They are attempting to refute the claim that animal farming is an efficient use of land.
"Much of the land used for animal farming, cannot be used for arable farming. With a rapidly expanding world population, a large proportion of whom are already starving, how can taking this land out of production help?"
This completely ignores the fact that large percentages of our corn and soy farming is used to feed animals. Ignoring this single data point either makes them ignorant or dishonest.