Yes, you're right. That first point was about the DIY cotton masks, not fluid resistant surgical masks.
Right, but even with a cotton mask the worry is hand-to-mask, not the other way around.
When you're out in the world, the potential concentration of viruses will generally be much greater on your hands than on the outside of your mask.
My understanding is that that's a misunderstanding (one that I was under as well).
For people who aren't sick, the worry is that your hands get contaminated (much more common, from surface contact), and then you touch your mask and transfer to the mask, and eventually it works its way in since these aren't N95s.
i.e. it ends up being the same as hand-mouth contact, but people think the mask is keeping them safe from that.