Apple-ply is very similar to Baltic birch- it will also tend to warp some- I don't know anything about cameras but I do know a lot about wood, so enlighten me- what is it exactly you are building?
If it is a box type structure, and the edges are joined, then the warp will be confined to a shallow bow between the corners , if it matters. Or it could twist slightly.
Thicker ply will be easier to join with a rabbet , glue, and pin nails , or thin pieces can be joined with a cleat , box joint, or stitch and glue- ( wired corners with epoxy fillet
For staying flat, it is very tough to beat MDF, it is not the strongest however. -but that may not matter for your application. It also paints well. If you need a flat, rigid, smooth, non resonant material this would be the ticket.