It is often assumed in special relativity that the rate of a clock in a non inertial frame does not depend on the proper acceleration of the observer. The point is, Rindler's observer shows us that the "action" of an accelerated observer on space-time is non trivial (there exists a black hole behind a uniformly accelerated observer). This means that there exists a way to discriminate accelerated observers from inertial ones. Moreover, Unruh's radiation explicitly depends on the proper acceleration $a$ of such observer (as a simple application of strong equivalence principle and hawking's radiation). This also shows that accelerating has a non trivial action on the whole physics observed. Proper acceleration being Lorentz invariant, it is also an absolute, so it is totally plausible that it changes whole physics and particularly clock.
Why should we believe in the clock hypothesis ? What would that implies with respect to strong equivalence principle and general relativity ?