I made my shed using his design and techniques. Every fall, when we stow away backyard furnitures, the umbrella, and Cycles into the shed with ease. I thank him.
I have a friend who owns a company that manufactures and installs metal roofing, and this is his professional opinion.
Searching, it seems to be somewhat contentious. Most --- but not all --- manufacturers recommend installing in the flat (usually with shorter screws at the ridge to join panels). Sometimes a distinction is made based on gauge and style of panel: very thin is always on flat, rounded corrugated is always on the ridge. Some local regulations though appear to require installing through the rib. Discussion here points to some of the advantages and disadvantages of both approaches: https://www.tractorbynet.com/forums/projects/179392-metas-ro....
If you find a firm manufacturer's recommendation for the style of panel that Mattias is using, perhaps email him? I think this is the sort of thing he'd be eager to get right.
As you said, it's also my understanding that the corrugated wavy stuff should be screwed on the ridges (that's how my friend did our sauna roof), not the valleys; and the flat stuff should be screwed on the flats, not the ridges. But I don't know whether nails have different recommendations (I imagine my friend would say don't use nails, use screws instead). I'm certainly not an expert, but my friend is.
I'd rather not contact Matthias though. I once wrote to him about some minor problem with his website (many years ago, way before his YouTube channel was popular), and his reply was rather mean-spirited and completely uncalled for. I don't hold it against him, but it's soured my opinion of him ever since. In any case, once you make holes in the metal, you can't really remove the screws.