The exact minimum are often a little arbitrary - but often in the wrong direction. The seller knows the fish is happier in a shoal, but also doesn't want to lose the sale - so what's the minimum number that could be a shoal but won't put of the budget conscious fish buyer/the one that wants to put as many different types in their tank - one is a single fish, two is a pair, therefore three is a 'shoal'. And like it or not, they probably make up the bigger consumer base than those that carefully research/care about behaviour needs and welfare.
There are a ton of scientific research articles on fish behaviour you can wade through. It's a bit hard to generalize as 'fish' is quite a diverse group. However, in general those that naturally live in shoals are less stressed if they are in shoals. They might not appear to interact much in a tank that is relatively small/not full of predators etc. but they'll know the other guys are there. Start swishing a net around and you'll often see them form up into a tight group.