Wait, what you said about fats and stuffs before doesn't makes sense. The energy from the sugars is going to be used before the fats will, so even if you eat just enough sugars to give you just enough energy, your fat will never be used.
Let's say you eat three croissants. You'd get a load of carbohydrates and some fats, of which the carbohydrates would be broken down into glucose and the fats into fatty acids. Most all this gets absorbed in the small intestine, entering the circulatory system where some of this glucose is used by the cells of your body to release energy via aerobic respiration, pretty much allowing your body to get shit done. At this point as well the fatty acids are used by the cells of your body like in insulating your neurons or in the construction of cell membranes, with the excess being stored as as triglyceride molecules - making up body fat. Simultaneously, you've just had lots of glucose enter your bloodstream and you can't use it all. This high glucose concentration is detected in the pancreas and insulin begins to be secreted by beta cells in the pancreas, stimulating the storage of this excess glucose as glycogen in the liver. If you eat even more croissants beyond your liver's ability to store this glucose as glycogen, it's just stored as fat.
After some time has passed and you haven't eaten anything, your blood glucose concentration begins to drop lower. Your pancreas detects this again and begins secreting glucagon, initiating the breakdown of glycogen into glucose in the liver for use once more throughout the body. When carbohydrates are scarce enough yet energy demands are not met by fatty acids from food (hence why hikers often carry the phatty bar to save their skin), the body begins breaking down its bodily fat reserves to release energy. If you endured under a croissant famine, your body would eventually even run out of its remaining fat reserves and glucose, at which point it would begin producing glucose for aerobic respiration by breaking down proteins in your muscle cells. If that goes on eventually your vital organs atrophy too much and you die. Diet is a balance after all :
D
Moving on you could have a constant supply of sugar and never begin to touch your fat reserves for energy but you'd sooner get diabetes. This is where diet is especially important (well, for most people it's not - it's mostly relevant for athletes and soldiers for whom reliable performance is paramount. For everyone else it's ""just"" vitally important for regular health). High carbohydrate diet = Go longer without touching fat reserves, slower regular release of energy regulated by the Pancreas; High protein diet = Shorter higher burst of energy, slower thereafter eating into those fat reserves. Best to have balanced obv.
In regards to your post, if you overeat and your blood glucose, liver stores and fatty acids are never scarce your body's fat stores will go mostly untouched and you'll get a net gain in body fat from anything that gets stored. So you're kinda right
Also, not what we were taught in school 
When it comes to education results may vary and curriculums are subject to dickery, political and lobbied. Sometimes it's just a case of simplification to make it easier to grasp/get pass grades/dumb down students
Like how in the UK our kids weren't taught how to code, with our IT instead teaching how to use Microsoft products. 10 secs guess as to who lobbied for this
Overeat = you get fatter
This is essentially accurate in 99% of cases. Unless you're going out of your way to only eat food with incredibly low calories (which is unhealthy anyway) you're going to get fatter from overeating.
100% of cases, if you overeat and gain more than you can burn, for as long as thermodynamics don't break that energy doesn't disappear
*EDIT
Oh yeah and fibre doesn't manage sugars. Soluble fibre may reduce cholesterol and makes poo softer, stopping constipation. Insoluble fibre acts as roughage, helping keep food moving through the gut. It also helps people avoid feeling hungry, useful if you're losing weight/are a fan of oats/in croissant famine
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