Your friend is correct.
It's not specular, because that would mean it's a mirror, and you'd only see the image if you were at the angle of reflection. Further, a mirror does not act as an image plane, so you might have difficulty ( :-( ) perceiving the image. Basically you'd need another lens to re-image the source.
The diffuse surface acts as an image plane. Each point in the plane radiates the incoming light in a Lambertian distribution. As such, it's essentially the same as a printed image, which as you know you can view from any angle by focussing on the image plane itself.