I think the reason for the advice to wear lighter weight trail running shoes, or hiking shoes is to inform the people who have not done the Camino yet that it is not all a technical type hike, and heavy mountain type hiking boots are not a necessity. A great deal of it is on improved surfaces (blacktop, concrete, etc). I would guess that notion that it is very technical is perpetuated somewhat by portrayals and photos of peregrinos all decked out like they are about to tackle K-2 or Everest. People see this and assume heavy hiking boots (and thick "hiking" socks) are needed.
Of course there are exceptions. I'm sure for some (people with physical conditions or old injuries) heavier, supportive boots are a must. But for the most part I would think that during the warmer, drier months of walking the Camino the lighter footwear works fine. Probably even more important than footwear is choice of socks and not carrying too much stuff in your pack.