Does special relativity tell us a physical clock will show time dilation?
For example, in the twin paradox, when the traveling twin returns to the earth, the relativistic time on the spaceship does have passed less than the relativistic time of the earth, but the biological age of the traveling twin is the product of the relativistic time and aging rate. When the relativistic time becomes shorter on the spaceship, the aging rate of the traveling twin becomes faster than that of the twin on the earth, which makes the biological age of the traveling twin exactly the same as that of the earth bound twin.
Similarly, a physical clock on the spaceship will have the same displayed time as that of the clock on the earth because the displayed time of a clock is the product of relativistic time and frequency divided by a calibration constant, and the dilation of the relativistic time is canceled by the increase of the frequency in the product to make the displayed times of the two clocks the same. That is, clock time (our physical time) is still absolute and won't change when observed from different reference frames.
As clock time is our physical time used in all observations, relativistic time is a fake time, and thus special relativity is wrong.
Is there any error in the above reasoning?