The data doesn't back this up in any country I can find.
A quick google search yields a few results, each pointing to the same conclusion:
https://www.cdc.gov/foodborneburden/attribution/attribution-...
> Meat and poultry, a combination of four animal food categories, Beef, Game, Pork, and Poultry, accounted for fewer illnesses, but for 29% of deaths.
Poultry accounted for the most deaths (19%); many of those were caused by Listeria and Salmonella infections.
This rate is partly due to three large Listeria outbreaks linked to sliced processed deli turkey meat; the last such large outbreak occurred in 2002.
Produce, on the other hand, accounted for 27% of deaths. However, it's important to distinguish here that produce accounts for 27% of all deaths, but animal products accounts for all of the rest. That's 73% of all food borne illness coming from animal products.
You are far more likely to die from food borne illness caused by animal products; especially agricultural animals.