Possibility of misunderstanding is most when Time dilation is seen as gravity or speed affected mass (as energy equivalents mass in E=mc2), than seeing it as gravity/speed affected frequencies (as energy equivalents frequency in E=hv).
What actually happens in the experiments as can be seen in the relationship λ∝T. The experiments actually need to consider dilated wavelength and not dilated time.
If the experiments consider that they observed dilation of time then it will violate fundamental properties of time. It rather would miscalculate T instead of calculating λ, because by considering changed/dilated values either of the value of the λ or even the value of T, one will get same result. But the illegality would be considering T as gravity affected consideration instead of appropriately considering λ as the gravity affected consideration.
A λ can be influenced by gravity and change its wavelength values but none can change T with the effect of gravity as time itself is not something changeable by any external interaction or influence unless such changes are in the structure of the events themselves, then only time comes into a relative consideration with the changeable events.
Time itself does not participate in any eventual act rather time tracks changes in the events. So a question of changing time itself is not only absurd but is illegal too as per valid definition and properties of time.
Time dilation necessarily needs to be wavelength dilation, when λ∝T comes in to the consideration.
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