It is not a fallacy. In special relativity the important concept is the frame of reference. For photons there is not no inertial frame of reference where photon will be stationary (relative or absolute means nothing actually).

The whole concept of measurement (which you will need to describe something as stationary) depends on an observer travelling at speed velocity less than speed of light. If you Try to assign a inertial frame of reference to a photon you will break laws of special relativity

- photons always travel in speed of light from perspective of any inertial observer whether it is moving or at rest (verified by experiment)

- relativity prohibited mass less particles (like photon) to be stationary.

E = mc^2 doesn't apply in photon and apply only on stationary objects. The complete equation is

E^2 = (p^2 c^2) + (m c^2)^2

Where m is the rest mass. In photon case the second terms vanishes and the energy is merely the first term.

-Time and space behave differently for photons. In relativity, time dilation and length contraction become extreme at light speed. A photon does not experience the passage of time in the way objects with mass do. Therefore, trying to define a reference frame for a photon would lead to contradictions in our understanding of spacetime.

So in general it doesn't mean much absolute vs relative on photon case.