The combination of the veneer and the glue (wetness) when it dries has
the tendency to cause any wood it's attached to to cup if applied to
only one side.

Agreed that plywood with its layers applied at cross angles minimizes
the changes of cupping, but it can still happen and I've seen it
happen.

Depending on how the 13 ply sheet of plywood is fastened down or if
it's purpose is panelling for a cabinet will go a long way to determine
if you really need to veneer both sides.