Though this is a tricky question, I believe that people can definitely be fat and still be healthy, but there's a limit to how fat. I think we as a society associate health with weight far too often. The people I've seen with the worst diets were skinny people or better termed, people who weren't overweight.
I know from experience, I ate terrible when I was younger and got sick more often than my peers, but my weight has always been in the normal range. Now I eat far more fruits and vegetables, deal with less sickness, and my weight is still the same.