1. If you look at the mithril armor in Oblivion, here are three examples of why it looks like metal - First, it is mostly chain mail; so even if someone were to find a silk that was as shiny as metal, try to twist silk into a type of rope-like configuration and then tie it together in a netting to resemble chain mail, in said configuration it would not be nearly as shiny anymore, and therefore would just look like gray netting, as opposed to the shiny metal of the chain mail in Oblivion. Second, the mithril helmet can't possibly me made from fabric due to it's shape/structure, unless the silk was layered on top of a harder substance like wood or metal. Third, there are various other components to the armor that, like the helmet, are obviously sturdy solid pieces of metal and not flexible fabric.
2. Arena had mithril weapons. If mithril is made from silk then it means the weapons would I'd either be really floppy (a silk sword? really?), or have to be a harder substance such as wood or metal, then wrapped in the silk. I just don't see that as making any sense at all.
1. Dunk it in some alchemist's concoction. That'd make it shine.
2. There is a silk staff in Jade Empire called Flawless, which is completely silk except for the blade affixed to an end. It was tempered by the sweat of a monk, I believe. Surely the Ancestor moths can concentrate really hard to get the right tensile strength in a strand.