While you are correct, rest mass of a particle which by definition must move is somewhat a useless concept.
If an object at rest has a mass M, moving at a speed v it will have a mass M/sqrt(1 - v²/c²). As an object approaches the speed of light, the mass increases without limit.
Because photons are light they are not at rest... they are moving at the speed of light. Therefore, since a photon travels at the limit of speed, it must either have no mass or relativity says it's mass is infinite.