Side note, I lost 80 pounds on a low fat diet, gained it back, then lost 80 pounds on a low carb diet so I know from personal experience.
I don't know the details of insulin and fat storage, but at the end of the day if you are at a calorie deficit, you will lose weight—that’s physics. Your body can’t magic fat out of nowhere.
Your point appears to be that some things are easier to cut out of your diet than others… which was very much part of what the parent said—they point out that calorie tracking is the best way to work out what foods are the ones that work best for you.
The point is not that all calories are equal from the perspective of sating hunger, but that they are equal in terms of energy input. Knowing that raw number for everything is the best way to understand what is providing you good “bang for your buck”.
None of this contradicts what you say, to be clear—it supports it, which is why I find it odd your post starts with “this isn’t true”.
The point is that saying that fat loss is as simple as calories in, calories out is unhelpful and not really true.
Also the whole point of losing weight is to be healthy. If you lost weight eating twinkies you might be skinnier but you are going to have a whole host of other health problems like high blood pressure, cancer, and heart disease.
The point stands that tracking calories gives you a defined goal. It's not the only goal for health, but that doesn't make it useless. The parent post you objected to was not claiming that what you ate didn't matter at all.
You are 100% right that healthy, sustainable weight loss isn't all calories, but weight loss itself absolutely is - and breaking the problem down into parts so people understand how to achieve that weight loss rather than having this arbitrary "healthy eating" idea that is much harder to track is a good thing. No one is advocating for it in isolation.
For most people, the eventual goal of losing weight is to keep it off, so the trivial truth that starving yourself inevitably leads to weight loss is unhelpful.