Yup, this is basically the only realistic way to avoid it, switch to types of food that cannot by their very nature have sugar added.

I would imagine most of those fresh vegetables have been domesticated/bred to increase sugars.

You're probably right, but that's still a lot better than manufactured foods. Also the funny thing with fruit and veg is that the opposite can happen, with the "Red Delicious" as the leading example, bred for looks and lost all the taste.

Even without human interference, fruit can actually be bad for you if you eat it at the wrong time and in the wrong quantities - fructose has the same effect as sugar - but now we are basically getting into nutrition more generally which is a tricky subject. Fruit still comes with many other nutritional benefits compared to sugary manufactured snacks, and even fibre that make it worth while (note that orange juice, as minimally as we are processing the fruit, still allows you to consume it in unnatural quantity and concentration, which can be very bad).