How does one reconcile those two sentences (neither of which I disagree with)? If one follows the CDC's draconian recommendations in that graphic you posted--which I guess is considered "not taking the chance"--one will be eating cooked-to-death food, and very limited fresh fruit/vegetables. No street vendor food. No ceviche. No paletas. No salsa. So where does one draw the line between "taking a chance" and "exercising a few common sense precautions"? Some precautions have been suggested upthread, such as eating food from vendors that appear to have a lot of customers, and eating only fruit and vegetables that have been washed at least in tap water if not filtered water. It sounds like those are common sense precautions to some of us, but taking (too big) a chance to others.
I guess you have to balance the options and decide for yourself, what are you willing to chance, and what will you avoid? You have to do that in life all the time, every time you get into a car you have risks - that doesn't stop you from driving, but it doesn't mean that you will take unnecessary risks, either.
I'm not a big fan of Mexican food in general, so it is not a hardship for me to avoid ceviche, paletas, and salsa. The fruits and salads and iced drinks and deserts are my big temptations.
The CDC didn't make up those recommendations just to be mean, they evaluated the travel-related food and water related illnesses reported for Americans and said "these are the best practices to stay safe" but there's still no guarantees. You might flaunt the recommendations and not have any problems, you might try to follow them but still get sick - or you could pick up an infection close to home and be perfectly okay while you travel.
According to the CDC, 38% of travel-related illnesses reported by Americans resulted from travel to Mexico - it's a big country and popular with US travelers. But the risks are still small that you will get sick at all - around 7% to 9%, and you are more likely to get ill in the less developed areas, unlike Cozumel.
Just try to be an informed traveler and do what makes sense to you and for your vacation. You have to take some risks if you want to explore the world, just do it with your eyes open. And if you do get ill, seek medical attention promptly.
I worked in downtown Chicago for many years and I never once ate food from the street vendors - it just doesn't appeal to me - so it is easy for me to take a pass wherever I am in the world.