It's a matter of how you read the statistics (a less charitable term might be "cherry-picking"). It's true that, if you are fit, your weight makes no difference to your health. Many athletes are classed as "overweight" (e.g. Aaron Rodgers has a BMI of 29, a stone's throw away from the obesity line) but most aren't at risk for the various diseases associated with weight (heart conditions, type 2 diabetes, etc.). This is true whether the extra weight comes from body fat or muscle (usually with people who are fit and overweight, it's from a mix of both).
Of course, most people who are overweight/obese are that way because they have poor lifestyles (sedentary, bad diet) and of course they are unhealthy. Additionally, even given people of comparable lifestyles, being obese seems to lead to some added health risks (overweight not so much), as does specifically waist size, although they're certainly not the significant factors and near as I can tell there's some debate as to how significant they are at all.
tl;dr being fat probably indicates bad health but the statement you quoted isn't, strictly speaking, wrong (though in the absence of further elaboration, I would call it misleading).
