Which statement about accretion disks is not true?

The statement that not all accretion disks rotate in the same direction as the star's rotation is accurate. Accretion disks can indeed form with a variety of angular momentum orientations relative to the star or object they are surrounding. While many accretion disks spin in the same direction as the central object, it is not a universal rule. Some may rotate in the opposite direction due to various factors such as the specific dynamics of material falling into the gravitational influence of the star or a result of interactions with other nearby objects or forces.

In contrast, the other statements highlight qualities that are generally true for accretion disks. The primary factor determining whether a white dwarf has an accretion disk is indeed its mass, as more massive white dwarfs are more likely to accrete material from a companion star. Additionally, accretion disks do form from gas and dust that is falling into a star, providing the necessary material for the disk's existence. Furthermore, it is common for accretion disks to be found around compact objects like neutron stars and black holes, as these objects are often the end results of stellar evolutionary processes that leave them with strong gravitational fields to attract surrounding material.