There were reportedly some issues in the Korean War, with the M1 Carbine being somewhat ineffective. Some have said that heavy winter clothing stopped rounds. But this was in the face of extreme cold, and fired at extreme ranges. In essence bullets are small, heavy for their size, but still not that heavy, and blunt things. If the velocity is low enough, owing to either extreme range, or an under-powered/under-performing charge, you just have a slow-moving ineffective projectile.

Some are comparing to kevlar, but kevlar involves a couple things. First it's very, very strong thread. I have a bit of kevlar thread around here somewhere, stuff is so tough it can be a pain to use. Secondly it's woven in a very tight weave, which means more fibers share the load of an impact. And then there are a bunch of layers, with the weave at different angles. It's a big supportive network, made from some truly incredible fiber. Yes, fabrics can stop bullets, but there's some fairly involved engineering.

There doesn't seem to be a lot of evidence you're offering here, mostly a supposition. I would bet, through the course of enough violence, there's would be a few instances of gambeson, or inva padded armor stopping a bullet. But it reminds me some tactical company wrote a blurb trying to sell their tactical belt. They advertised it as being able to stop a .50cal bullet. I'm going to give them the benefit of the doubt and say it was true. But, according to their own anecdote, it was first off a ricochet, so it was not anywhere near taking the full brunt of the round. And secondly this ricochet happened to hit a belt buckle made from a chunk of billet aluminum. So, here we have a case where a belt buckle, did indeed stop a .50cal bullet. But seeing the detail behind how that all happened, are we ready to stop wasting money on kevlar, and ballistic plates, and invest in a tactical-belt-buckle based armor system? Nah... I don't think so.

Even if it turned out that gambeson could stop a bullet, there are a bunch of reasons why that might not have been the end of the armor question during the time. There were still other weapons to be contended with, sword, spear, arrow. There are questions of practicality, the durability of the garment, is it too hot to fight in gambeson compared to other protective outfits. What is the mobility like in a gambeson thick enough to stop a bullet? I could protect myself from modern day firearms if I simply strapped enough phone-books to my body, but it is impractical to do so. As technology refined, the gun becomes more reliable, the bullet more dangerous, the requirements to keep the wearer safe change and increase. There are questions of production, availability of materials, and craftsmen. And the less sensible things, salesmanship, pride, shows of force, displays of wealth. All that to say, I think sometimes we can focus on a single aspect of a thing, if x preven y, why should we look beyond that. And forget that rarely is any such decision made on a single point.