A lot of people believe this, but it is incorrect. In plywood, the glue transfers the load across the faces of each ply from strand to neighboring strand through the adjacent plies. This can result in a stronger bond between neighboring strands than if no cross-plies were present. This amounts to more than just splitting resistance.

As a parallel case, consider multi-ply composite construction, where sheets of fabric, sometimes of sheets with a single fiber orientation, are laid at angles to each other to spread the loads in exactly this way. They both better approximate an isotropic material, and are stronger than an equivalent thickness of singly-oriented plies all in the same orientation.