It's a little difficult to tell from your photos for certain, but what I'm seeing does not, to my eye, appear to be silk. Silk intersects at 60 degree angles, per the hexagonal growth of sapphire crystals. If you look carefully at your "spiderweb" these lines almost universally follow the girdle around the stone--varying in their angles of intersection--as more facets are present in a tier around the stone. I think these lines may represent polishing marks on the surface of the facets themselves--in other words, little grooves on the facets. Although I could be wrong.
It is important to note however, that while the presence of intact silk suggests unheated status, it is not a guaranty. Stones may be heated under lower temperatures that do not entirely disrupt rutile needles.
I'm sure a gemologist could direct you better.