Summary: Relativistic effects cause errors in clock oscillations and therefore establish time as independent of eventual influences. So under the relativistic effect the clock does not run slower than the observer's clock but it causes errors in reading the time.
Relativistic effects on the phase shift of frequency cause errors in clock time readings and therefore invalidate the concept of time dilation.
The error establishes time as independent of existential events, and therefore under relativistic effects the clock does not move slower than the observer, but causes errors in the clock's time reading.
