There's a huge difference between having your digestive system in operation (i.e. stomach acids, spleen, pancrease, gall bladder, peristaltic movements, etc), or having them dormant. When you are eating something, all your digestive organs are in operation. And, just like any other organ in your body, you need to fuel the operation of your digestive organs. It's the "price of doing business" with your digestion. So, as example, when you eat a piece of bacon, you chew, swallow, stomach juices digest, organs (pancreas, gall baldder, etc) secrete enzymes, etc. All this activity doesn't come "free". At some point, all your digestion organs need fuel/blood/heat/power/etc.
But...when you are fasting...like...only water/tea/coffee...your organs go into dormant state. Your pancrease, gall blader, stomach juices, etc...are not needed. All the calories/energy/fuel etc they need in normal eating operation is severely dialed down. Your body is smart...recognizes that there is "no need to keep the lights on" in your digestion system, and keeps everything on very low energy expenditure. It's like if you go on a 2-month vacation, you unplug all your appliances, turn off every light, you turn down the heat/air conditioner, etc, just to avoid wasting energy in your home for nothing.
However, if you "cheat" on your extended fast, and eat a little bit of something, then you start screwing everything up. Because, now your body has to turn on all the organs for digestion, but to process very little calories. It's like driving your car to go get gas at a station that is 100 miles away, but you only have 60 miles worth of gas left in the tank to get there. So, your body starts to freak out, and turns down your metabolic rate...it looks for other places in your body to "steal" some energy from, to keep your digestion system operating properly...because you cannot half-ass operate digestive organs, or else you die. There is minimal work that your body has to do to clear whatever food you swallow...or else, all hell breaks loose in your digestive system, and it can kill you. So, if you do not properly fuel yourself, you will feel more tired and have less energy to do other stuff (like biking, hiking, staying up late at night, etc)...that's your body turning the dial down on lower-priority body functions to ensure your survival.
So, the best thing to do is fast properly. Don't cheat and eat a bit of something when you are fasting...or else, you will turn on your digestive system, without sufficient fuel, and it then forces your body to turn down your metabolic rate.
So, when you fast, your body goes into ketosis and autophagy...breaks down its own tissue for survival. It first scavenges all the bad tissue extra fat inventory...but...when that runs out, it has no choice but to start scavenging good tissue. Usually, this is not a problem (as obese or overweight people, for example, do extended fasting to help get rid of extra body fat). But, for thin people, extended fasting is a challenge. This is why they may supplement with oil or butter, to stay is fasted state, without scavenging good tissue. They can supplement with something that is very digestible (like MCT oil), so again, not activate the entire digestion operation, so as not to provoke the body to lower metabolism.