You make a really good point, and simply put, I don't think there's a definitive answer. I've never run into any contemporary descriptions of medieval tanning, even from times and places where tanning was almost certainly practiced. And archaeologists don't often look for diagnostics that could be used to prove leather-making unless it's plain like at Portmahomack, where they found a stone pool next to a line of animal hooves (showing that skins had been cleaned and washed there).

I think it's entirely plausible that medieval peasants would turn hides into buckskin, which like rawhide requires less of an intensive chemical process than tanning. Once the hide is cleaned, it is simply dressed with a solution of ash and possibly other materials (like animal brain or egg yokes), which keeps the hide soft and pliable. It may then be boiled to add firmness. Rawhide is similarly made using lime (taken from limestone or chalk) instead of ash, but this produces a hide that gets brittle when dry. Buckskin would be useful for clothing or bags, whereas rawhide would be useful for building more solid objects (drum heads are the most familiar).

Leather tends to require a bit more work. Unlike buckskin and rawhide, which receive only a superficial application of lime or ash, good leather must be completely soaked in the tannic acid (i.e. the solution penetrates the entire substance). The advantage is that it becomes completely waterproof and won't putrefy when it gets wet, whereas buckskin and rawhide can rapidly deteriorate. For hunter-gatherer societies who produce an abundance of hides, this rapid deterioration isn't a problem. But for sedentary agrarians in the moist climates of northern Europe, it would be a concern. Leather may also be boiled to make it harder, which is especially good for armor and book bindings.

OP's question and some of the other discussion has been specifically about armor. Rawhide would be too brittle, buckskin too soft and ready to deteriorate. (Although I'm aware buckskin has sometimes been imbued with apopotraic qualities, like a protective amulet.) Boiled leather is the best option, and I still think it's reasonable to assume that few peasants would have had access to the necessary materials or facilities, much less the practical knowledge or the available time, to have leather armor.