"Those who pick the vegetables have no documentation and are generally migrants."
I think you confused "migrants" with illegals.
There are legitimate federal guest worker programs used in NC to bring mexicans (migrants) to the fields for the growing season.
They may use them in Florida as well, the only problem is there are two or three growing seasons in Florida so temporary work is actually year-round.
Of all the trades, I'd expect that farm labor would have the highest percentage of illegals. But maybe not, I don't know. BTW when I used the term 'migrants' that was not a statement of their legality, I meant only that they move around from one farm harvest to another, they don't put down roots.