Cooking causes certain chemical reactions within the food being cooked, many of which produce (and consume) compounds which have various flavours.
I don't know the real specifics, but I can outline why your two cases are different, and you can verify it visually. If you take a potato, cut it up and boil it, it stays pale. The texture changes to become much nicer to eat, and the flavour loses that raw starchiness that raw potato has (ever eaten raw potato? I don't recommend it...)
If you take that same potato (or, for realism's sake, a very similar potato) and cut it up and put it on a baking tray and put it in the oven to roast, what you get out has golden brown edges and a different texture, and a bit of a skin over the surface. Why? Ovens apply heat differently. Inside your oven is air at 200 degrees C or so. This is much hotter than the water in a saucepan (which caps out at 100C at sea level unless it's a pressure cooker). So the first potential difference is temperature - some reactions simply do not happen at the temperature you can achieve while boiling.
The second difference is the environment. If a reaction relies on one of the gases in the atmosphere to happen (chances are it's oxygen), this is not going to be the same when the food's submerged in water containing far less oxygen than the air does.
So when you roast your squash in the oven, you're allowing reactions to happen which cannot happen if you boil it, thus leading to different flavours. Particularly relevant is the Maillard reaction, which requires a kind of fat and sugar and lots and lots of heat, and happens when you brown meat in the frying pan, or in onions being roasted in a hot oven. It's a complicated business that has many different possible end products, some of which can then react further to make different ones again... read about it on Wikipedia if you're interested in the details. The point is that there is no way to get those flavour compounds at temperatures too low for the reaction to happen - Maillard requires about 155C, well over the boiling point of water at sea level. There's also caramelisation, which is a different flavour-producing reaction.
I guarantee that if you make two batches of soup, boiling one and roasting the other, you'll find that the roasted one tastes quite different. That doesn't mean you can't make nice soup by boiling raw vegetables (I've done it), but you can't make the same soup.
Once you start thinking in terms of techniques, it shouldn't be that hard. The book Ratio has an excellent overview of different methods for cakes. The blog pastrychefonline.com does as well. You can see an overview of the:
- Creaming method in which softened but not melted butter and sugar are whipped together first to create a network of air bubbles for structure, then eggs, if called for, and other liquid ingredients added, then (or alternated with) solid ingredients. Overmixing after a certain point destroys the air bubble network, but you need to build it up well first. An alternative is the Two-Stage Mixing Method in which eggs and flavoring go in with some of the liquid, then softened fat and solids all get added in, then the rest of the liquid in parts with little mixing.
- Foaming method, or sponge cake in which egg yolks and whites and sugar are whipped together to form the air bubbles, then dry ingredients are added, then melted butter is added at the end if called for. I believe in Ratio butter is added before dry ingredients, but I don't remember if that is the case. Again, you don't want to start popping your air bubbles.
- Biscuit Method or pastry method for pie crusts and biscuits, in which it is important to keep your fat very cold and leave some larger pieces of it for flakiness and usually over mixing after liquid has been added causes a dense biscuit or crust because it activates the gluten.
- Muffin Method or quick cake/bread method in which all the dry ingredients are added to all the wet ingredients and the fat is melted or liquid as opposed to softened or cold. In this case leavening comes from commercial leaveners instead of mixing so at no point do you want to overmix and activate the gluten.
- There is an exception for batters like crepe batter where there is simply so much liquid that the gluten will never be activated. You can mix a high liquid content batter all day if you want.
And not covered on that blog are:
- Yet another technique uses whipped egg whites only for structure, much like making a meringue. I have a waffle recipe that uses whipped egg whites at the end for additional structure after using the muffin method for the rest of the batter.
- For bread I personally love the explanations in Peter Reinhart's books, both that on regular bread and also whole grain bread. You WANT to activate the gluten, so that's why you knead it after mixing (or in the case of the no-knead bread movement let the yeast activate it over a very long time), which is basically more mixing. The structure of bread is a combination of the bubbles from the yeast and the gluten that is partially activated by kneading. After rising you want to handle even bread gently, though, so as not to degas the yeast bubbles.
There may be more and different recipes use different variations, but these are the ones that spring to mind. The key is to figure out:
- How is leavening happening - from chemical leaveners, a mixing method, steam during baking, yeast, or a combination of these?
- How much do I want to activate the gluten?
The answers to these two questions largely determine the temperature of your fats and eggs and how much you mix.
Best Answer
You seem to be mixing up three things in your question: the total amount of fiber, the degree of mechanical change to the fiber, and the health effects of eating fiber which has been mechanically changed.
For the first, the answer is clear cut: there is no change at all in the total amount of fiber. Blending is not a chemical reaction, it won't turn inulin molecules into anything else any more than grinding lead will turn it into gold.
For the second, it is unlikely that there will be a single answer. First you have to define exactly what kind of mechanical change you are interested in, and for any of these changes, to live with the fact that all accompanying variables (what blender you have, how long you turn it on, what are the other ingredients in the recipe...) will change the answer quite a bit. And you yourself found a specialist saying that people don't seem to have studied that.
The third is simply off topic here. Any answer based on the health effects of mushrooms, either telling you something about them directly, or choosing how to answer the amount-related second question ("there are many types of mechanical change, but only type X is interesting from a health point of view, so we will tell you the amount for type X") is out of scope and will get deleted.