It is true that – implicitly throughout history, and explicitly since at least the time of Galileo – humans have tended to assign ontological status to the measures of time and space corresponding to what we now call standard inertial coordinate systems – in terms of which inertia is the same everywhere and in all directions – and on this basis people sometimes say (speaking loosely) “time runs slower for moving objects”. But this is really just a casual way of saying “given two standard inertial coordinate systems (x,t) and (x’,t’) moving with a relative speed v, the rates of change of t’ with respect to t at constant x’ and of t with respect to t’ at constant x are both equal to the square root of 1–(v/c)²”. This is a mouth-full, so it isn’t surprising that people who understand special relativity often revert to shorthand expressions – even though those expressions can be confusing to those (like Bethell) who don’t understand special relativity. Setting aside the semantics, the question of whether or not someone chooses to regard the time coordinates of standard inertial coordinate systems as representing “time” in some metaphysical sense is, well, metaphysical, and has no bearing on the validity of special relativity. Again, the entire content of special relativity is that all physical phenomena are (locally) Lorentz invariant, meaning that standard inertial coordinate systems (in terms of which inertia is homogeneous and isotropic) are related by Lorentz transformations. From this follows all the relativistic consequences of length contraction, time dilation, and relativity of simultaneity in the sense of inertial coordinate systems.

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