I imagine that as with so many things concentration over time is the only difference between a neutral compound, a medicine, and a poison. Almost every compound is a toxin at some threshold, eg. NaCl, H2O…
Yup, nitrates/nitrite are added to meat, my guess is at higher concentrations than what is found in plants. There is also the possibility of differences due to formulation and potential derivatives eg what happens to nitrates when cooked at high temp in fat/oil in terms of human absorption and any derivative products or precursors that might evolve in those conditions that aren’t typically used when preparing veggies. I don’t know the answers but these would be things to look into.