Not really no.
I'm not saying eating a bit of cow poop on your lettuce never gets anyone sick, but that's not the mechanism of concern.
One: poop is mostly bacteria, by mass. It isn't infected with ... it is. Some can be "pathogens" but that's what the last stage of digestion is, fermentation with mostly a wide array of bacteria.
The concern is these gut bacteria developing antibiotic resistance and bacterial infections in the animal developing resistance. Then infections are spread between animals and across species and the waste is reintroduced into the environment. Resistant bacteria in the environment share. Horizontal gene transfer between species of bacteria can lead to these resistance genes being popular and everywhere. It's not cow poop infecting you, its the genetics getting spread into the environment and eventually ending up in a human pathogen.
>animal waste is sometimes used as fertilizer
More or less all industrial farmed animal waste ends up as fertilizer. Also a major component of the kinds of soil we grow crops in is bacteria, much of which has been through the digestive system of an animal. Again I don't know what people think soil is. If you want "clean"(?) never been poop growth medium for your plants you have to go completely artificial. And manure isn't sterilized before it goes into fields, it's alive.