I must say that this statement is deeply wrong, the invariance of the speed of light in fact *destroys* the invariance of the "speed of time". In Newtonian theory the "speed of time" is the same for all observers, so their clocks never get out of sync and one can speak of "universal time". In SR the "speed of time" is different for different observers, so although they each feel like time is passing at the same speed as it always does, their clocks can nonetheless get out of sync (if they bring them together at one location and compare them they can end up different in SR).
The thing that seems to be so hard to understand is that IMO you can put a dilated clock and non dilated clock or any clock regardless of dilation side by side and yet they still share the same present moment. [ as time passes through them side by side at differing rates.] the present moment [HSP] being in effect, stationary on the time line as time flows through it.
I suppose that was Newtonian as well?
Say for the sake of the discussion we asssume for a moment that time is absolute in a Newtonian sense and that the photon is always in existance only at the present moment between future and past.
However we also understand that the speed of light is invariant and that time flows through the present moment at that speed [ 'c' ]
We agree that a future photon can not exist nor can a past photon exist as they can only exist in one moment of time that being the present moment.
This means then that the present moment is also our
inertia constant as time flows
through this moment at an invariant rate of 'c'
So through out the entire universe every single light event must occur in the present moment thus the present moment is absolutly the same universally as determined by the light event and not by the observers relative velocity or clock tick rate [ remembering that clocks are usually mass premised]
There is absolutely no reason for time dialtion effects to accumulate*** and force a relative simultaneity [relative zero ] situation upon the universe and whilst the clocks tick rate may vary due to dilation the underpinning change rate that generates the platform for the clock is constant because dilation is physically necessary to maintain that constancy.
Therefore it could be proposed that dilation is the universes way of ensuring change rate [ invariance of 'c'] constancy and the constancy of the universal present moment HSP] is maintained.
Therefore it could be further proposed that time dillation is an effect caused by inertia.
** the only possible reason could be our "flying pig" called photon that has never been served for breakfast.
The presumption of a travelling photon must necessarilly lead to SRT. As there is no evidence to support the existence of a travelling photon then one has to wonder why we rely on such a theory as SRT when better theories would suffice that do have evidence and don't make such presumptions.