Part of the confusion also lies between what the "welcome to the US" video shows while you are waiting for immigration (at least in Boston) and the custom form.

The video seems to imply that only fresh products such as vegetables and meat are forbidden whereas the custom form asks you to declare any food.

For my last entry, I did not declare any food but had 24 cans of tuna in olive oil and was controlled. The officer told me I should have been honest on the form but let me keep the cans...