It's a load of crap.
Here's some data from the CDC regarding obesity rates according to age group: http://www.cdc.gov/nchs/fastats/overwt.htm
As you can see, the rate drops by 2% for the "high school age" demographic compared to childhood. However, this basically doubles for adults over the age of 20, which indicates that any mitigating effect in high school was lost. Furthermore, another 34% are overweight, which means we are now at 68% of the adult population being above a healthy weight. There is no way one can make any convincing argument that PE in high school helps stop obesity, as the increased trend from childhood continues into adulthood (shit, even the doubling trend continues!). If anything, I would attribute the slight decrease in adolescents to peer-pressure, but I can't find any data to back that up. Yet.
Now let's examine adolescents individually. Here's another study: http://www.cdc.gov/nchs/data/hestat/obesity_child_07_08/obesity_child_07_08.pdf (interesting data is on the last page)
What we find is that obesity rates have increased over time, and that more males tend to be obese compared to females of the same ethnicity, save for African-Americans. Given that that sports and PE in general are geared more towards males, this would indicate that such programs have no statistically significant effect, although attributing the on average lower obesity rates of females to peer-pressure is once again a viable, although not yet statistically backed up alternative. What I see as a more likely explanation is the income discrepancy of the ethnicity compared. Here's the average income by ethnicity from 2005, which will suffice for a topical comparison: http://factfinder.census.gov/jsp/saff/SAFFInfo.jsp?_pageId=tp6_income_employment. What we see is that of the three groups compared, whites make by far the most (go figure...), whereas blacks and Hispanics only make about 60% of that income. While Hispanics have a slightly higher average income, they also have *on average* larger families (http://www.ers.usda.gov/publications/aer731/aer731d.pdf), which leads to n overall lesser income per family member. Given that fast-food is on average the cheapest meal option (here's a fun article showing $/calorie of some fast food items: http://articles.moneycentral.msn.com/SmartSpending/ConsumerActionGuide/wallet-vs-waist-fast-food-cost-per-calorie.aspx), it is reasonable to assume that households with the lowest income per family member are more prone to eating the cheap but fattening fast food. This type of behavior continues on into adulthood, where it then impacts the next generation. There, that seems the most likely explanation for why obesity is so prevalent in the US.
Want to alleviate the problem? Replace sodas in school vending machines with water/sugar free tea/diet-sodas, make school lunches healthier, do not have those stupid snack vending machines, and have some real fucking nutrition lessons in that otherwise completely worthless "health" class. The claim that PE helps solve the problem is not backed up by statistics. On that note, the education system here is shitty enough. Might as well replace that PE stuff with some mandatory "how not to be a worthless idiot" course.
This little rant was written by a 179cm and 68kg white guy and recent college graduate who is in better shape than some athletes out there. How you may ask? About three hours per week working out (running/biking), and a dozen sit-ups/push-ups in the morning and evening. Oh, and healthy eating, but that vegetarian thing ain't for everybody it seems...
