I've just started remodeling a tiled shower. According to a video I saw
on line, once the tiles have been removed the screws holding the backer
board to the studs should be visible and can be removed, thus allowing
the backer board to be removed.

I've removed the tiles from one section, but there is no sign of any
screws. I was able to get a pry bar under an edge and pry it off,
revealing nails whose heads were tight up against the mesh and driven
into the wood, but with no hole on the surface and no evidence of a hole
having been filled after the nails were driven in..

Further, either the backer board was somehow wrapped around an outside
corner -- and with good clean straight edges -- or someone had managed
to cut a clean straight edge in the cement part, leaving the mesh to be
wrapped around the corner and nailed under the backer board on the
adjacent surface. I don't know which, as I haven't yet removed the
backer board from that second surface.

Perce