Is a species lifespan affected by meat consumption?
I don't think that the theory is very reasonable, because animals drink from stagnant ponds (i.e. savanna wells , forest puddles) and have lots of vectors of infection other than rotten meat: cuts and grazes, tract infections, parasites like mosquitoes and nematodes.

The olfactory sense is also very sharp in many carnivores and they can gage the decomposition state of meats. Even humans have a very strong sense of the age of meat using smell, although I can't find  research on it. 

The fun thing is to see the age of other animals, i.e. birds and bears. The oldest zoo birds:  

Flamingoes, seagulls, vultures, 50-70
parrots 90-120 years. 

the oldest panda: 37
the oldest grizzly and polar bear: 40 and 42

Oldest reptiles:
lizards crocodiles and tortoises: 50-100 years
giant tortoise: 150-250 years. 

Other herbivores with slow senescence: donkey 60, bison 50, gorilla 60...

research papers don't include any evidence to correlate carnivory and lifespan. It's mostly body mass and ecology, i.e. predation rate. 

Carnivores have must stronger stomach acid also which mitigates some of the risk.