Consider a projector pointing perpendicular to a plane. Its projected area will be a square, or perhaps a rectangle. Depending on the distance between the projector and the plane (and the projector matrices) the resulting image to project will have to be minified or magnified.

Ideally, we want to keep the pixel mapping 1:1.

Now, move the projector away from the plane (keeping the camera in place)

What happens is that the projected texture (the problem is not shadow-map-specific) will have to cover increasingly more pixels of your viewport / plane. When the texture has to me magnified, you have projective aliasing because the distance between adjacent pixels "on the screen" once mapped to the projected texture are more distant than 1 texel.

In other terms, 1 projected texel ends up bigger than 1 pixel (or the defined threshold).

In general, perspective aliasing is discussed when considering oblique frustum but I don't think it's necessary.