With sexual organisms, mixing of genes means that each offspring has a different set of genes, and so each individual may have a different cell surface. This makes it much harder for parasites to evolve effective invasion techniques. This is the other plausible benefit of sexual reproduction. They are not mutually exclusive. It is a trivial exercise to test if an organism is occasionally asexual.
Many organisms have that capacity.
The difficulty is in demonstrating obligatory asexual reproduction. As noted above, many organisms once thought to be asexual are now known to be at least occasionally sexual. Enter the bdelloid rotifer. Bdelloid rotifers are so small that they are best seen under a microscope, where their translucent bodies glitter as they swim. They may be microscopic, but they are animals, like elephants and insects and birds.