So, this is a topic that is near and dear to my heart as my undergraduate research was funded, in part, by the CDC. Anyway, whenever the topic comes up and people are trying to figure out what happened I direct them here to learn more:
https://www.fda.gov/food/foodborneillnesscontaminants/foodborneillnessesneedtoknow/default.htm
Now, one thing to know is that everyone in your party could have been exposed to a food-borne pathogen but only those that have a particular susceptibility
at that time would have a physical manifestation of symptoms. Generally, our most vulnerable age groups for falling ill to these pathogens are the very young, the very old and those with a compromised immune system - and that group can be anyone whose immune system is already working overtime fighting off something else, like a wicked cold, or working hard to build another human, ie. pregnant women (This is an
opportunistic infection as your immune system might have fought it off handily had it been working up to par).
I'm sorry your son got sick. I wouldn't wish a food-borne illness on my worst enemy, especially an E. coli 0157:H7 infection, and while beef is a common vehicle for that particular pathogen, without some lab work to determine the exact pathogen involved it is purely speculation what exactly happened.
So the bottom line: Yes, it can happen but don't let it keep you from living your life and enjoying your vacation. And if you do come down with a food-borne illness, palliative care is usually sufficient but sometimes medical attention is warranted so just keep that in the back of your mind.