read the stuff again. overeating will lead to obesity in most cases, where there isn't some disease/condition preventing the fat accumulation, in which case the person isn't really overeating anyways.
But, you could think it from the other way - without overeating it's __impossible__ to become obese. .
Unfortunately, this is well-documented as not being the case. Our "common sense" screams that it's true, but it's not, and so we really have a hard time letting go of it. :) You can start reading about it by Googling "obesity malnutrition paradox" (some of the links will take you to malnutrition via overeating, I'm not talking about those, but there are oodles of resources about obesity in populations where there are nowhere near enough calories to reach what is considered the minimum recommended daily intake). What's particularly compelling is that the same scenario is documented in many different peoples/societies in many different time periods - so it's incredibly well-established that obesity can and does occur without excessive caloric intake. Also, there are an abundance of studies that refute the notion that overeating *causes* obesity - there is a correlation, yes, but there isn't solid scientific evidence to support a causal relationship in the way you indicate (although there is a good bit of evidence that shows a causal relationship in the other direction - obesity leading to overeating).
statistics back this up (counting out exotic diseases, elephantinism or whatever). besides, it's a proven method for losing weight: eat less, do more - or inversely a proven method for getting fat: eat more and do less.
Actually, no, there is a strong tie between eating less / doing more and feeling hungry, but not between eating less / doing more and losing weight and keeping it off for any interesting length of time. A really interesting link though is that the rise of the "eat less / do more" philosophy (as a way to control weight) more or less exactly correlates with the obesity epidemic - not saying it caused obesity, but that those ideas as a means of weight control replaced earlier, more correct ideas, and that transition in thinking also marks the rise in obesity. Similarly, there is strong evidence that the introduction of the food pyramid with a high carbohydrate base has been particularly disastrous. Prior to both of these philosophies, it was fairly well-accepted that carbohydrate intake and obesity had a causal relationship, but these fell out of fashion... and obesity rates took off.
(and it doesn't really work like a river that it takes what it needs, it takes what it can and figures out where to put it later).
This too isn't quite right, unless you for some reason don't poop and pee. A really obvious example is most types of fiber - for the most part fiber passes right through your system (which, incidentally, is why e.g. a diabetic can for the most part ignore fiber when counting carbs to predict glycemic impact of a meal - the vast majority of the fiber isn't metabolized into sugars and just passes on through). Maybe that's what you meant by "takes what it can", but just because a calorie is introduced into the body, it doesn't somehow force the body to hang onto it - the body is quite adept at giving off what it doesn't think it needs (hint for what follows below: the problem isn't that the body doesn't know what to do with excess calories, but that it is being quite directly told to hang on to too many calories). Further, all calories aren't created equal - simple sugars, especially those already in liquid form, get sucked up by your body much more easily than the calories that are in the small, digestible portion of fiber.
Perhaps the misconception is because it's easy to assume that e.g. eating a fatty or high calorie food means more fat will end up on your body. That's not exactly how it works though - your body contains fat tissue that is used to store energy in the form of fat. It's like a rechargeable battery and is a necessary part of a normal, functioning body - it's what you need to survive the night without eating constantly, for example. Fat stored in fat tissue doesn't come from fat in food per se, or even directly from the calories in food (as in, it's not that direct of a relationship). The more correct (but still simplified) process is closer to: intestines metabolize food into sugars and deposit them into the bloodstream, insulin in the bloodstream acts as a trigger to the fat tissue to remove sugar from the bloodstream and to store it as fat. The reason many types of carbohydrates contribute to obesity is because they are often a double-whammy: many carbs contain high amounts of simple and easily digestible sugars *and* carbs trigger (often by a huge amount) rises in insulin levels. In a nutshell, a high carb diet tells your body to go nuts storing energy as fat and gives your body an excess of energy that is particularly easy to stockpile - very little "effort" is needed to extract it.
OTOH, many, many calories can be present in types of food that are more difficult or even impossible for the body to metabolize, which is why if you eat 2000 calories and burn 1500 calories, it doesn't *at all* mean that 500 calories must be stored by the body as fat - some or even all can be released from the body via waste (it's gross to think about, but both urine and feces can contain huge amounts of calories).
So back to the idea that without overeating it's impossible to become obese, the reason it's not right is at least in part this: obesity comes as a result of your body being told to store too much energy as fat, but an excess of calories does not necessarily translate into your body storing them as fat, nor does your body storing energy as fat depend on an excess of calories (the fat tissue can actually compete with e.g. the muscles for the sugar in the bloodstream, such that the person is nutritionally underfed but still accumulating fat).
Anyway, an active lifestyle and healthy eating are both extremely important and beneficial. They don't, however, help very much with obesity.