I never claimed that we weren't unhealthy but that being unhealthy isn't "American culture" as evidenced by different demographics in America having markedly different obesity rates. The obesity rates are similar among similar demographic groups in different countries - e.g. white people in the US have similar obesity rates as UK, Canada, and Australia. It's very weird to say that this thing that is constant among demographic groups across countries is dependent on the culture of one country. Especially when it is different among demographic groups in the same country.
I am not implying that white people are genetically predisposed to obesity. Actually, what I wrote is the exact opposite. I suggested the obesity rates were due to environmental factors and, crucially, I pointed out that other racial groups have greater obesity rates. So, I explicitly stated I believed the difference was not genetic and that white people have less obesity in the US than non-white.
For the other points you seem to prefer using a different metric, overweight instead of obesity. You haven't said why that factor is more relevant or how it changes what I wrote above.
However, being physically active makes you more aware and mindful of the input side of the equation; building muscle mass, cardiovascular fitness and endurance in turn improves your metabolic ability to burn calories. So it's absolutely part of the picture. "The Miracle Pill" by Peter Walker is an excellent introduction to the topic.
You've listed the obesity rate, not the rate of people who are overweight. Beyond that, you haven't limited to adults. According to the CDC [1]:
Percent of adults aged 20 and over with obesity: 42.5% (2017-2018)
Percent of adults aged 20 and over with overweight, including obesity: 73.6% (2017-2018)
It absolutely has to do with lifestyle. America is one of the cultures most reliant on cars in the developed world. Physical activity is also ridiculously low. The problem is there's no way to reliably measure physical activity across countries. There's just survey data, and people in the US know they _should_ exercise.
[1] https://www.cdc.gov/nchs/fastats/obesity-overweight.htm