The headline says farmers. The text says farm workers. Very much not the same thing. A farmer is the owner of the farm. A farm worker is generally a hired hand, often (though not always) a migrant, and if so typically from Mexico or farther south.
The story suggests that the multi-drug-resistant bacteria are the result of antibiotic treatment of the animals at the farm. This misses another possibility:
In Mexico, most antibiotics are over-the-counter, much like asprin here in the US. People who feel ill or have some infection often buy and take them. Typically they use them until they no longer show symptoms - then stop, rather than taking a full regimin and killing off all the bacteria. (Why take more of the non-free drug once the symptoms are gone? Waste of money, right?) This is a recipe for creating drug-resistant bacteria.
Of course if an infection is resistant to one antibiotic, a paitent is likely to try another, and another, and so on until they find one that works. THAT's a recipe for maintaining and improving the bug's resistance to the front line antibiotics while breeding resistance to others.
As a result, a substantial fraction of the workers arriving from south of the Mexican border are carriers of multi-drug-resistant baceria.
Meanwhile, a farming operation is likely to give a limited number of antibiotics continuously, so non-resistant infections are wiped out before they can develop resistance, and if they do develop resistance it will be to the particular drugs used, rather than the universe of antibiotics.
Of course, infected workers can infect livestock, just as livestock can infect workers. And infected workers can trade infections around, just as livestock can. (More so, since the livestock tends to be kept separated, to reduce both disease spread and breeding by unintended pairings, limitations that farmers can't impose on their workers - and would be unlikely to try even if they could.)
So it seems to me that responsible researchers would go a bit farther before reporting: Like by doing genetic testing on the strains of bug in the various workers and the livestock, and running models on the results to try to identfy whether the bugs are from the herd or the workers.
I don't see any such work alluded to in this popularized reporting. It seems to just assume that the bugs were developed on the farm and spread to the workers. I hope this is a disconnect between the actual research and the report, rather than an accurate characterization of the research.