In a recent research study entitled “Test of Time Dilation Using Stored Li+ Ions as Clocks at Relativistic Speed” (Phys. Rev. Lett. 113, 120405 – Published 16 September 2014), an Ives–Stilwell type experiment, it was claimed that a conducted time dilation experiment using the relativistic Doppler effect on the Li+ ions resonance frequencies had verified, with a greatly increased precision, the relativistic frequency shift formula, derived in the Special Relativity from the Lorentz Transformation, thus indirectly proving the time dilation predicted by the Special Relativity. The test was based on the validation of an algebraic equality relating a set of measured frequencies, and deduced from the relativistic Doppler equations. In this study, it was shown that this algebraic equality, used as a validation criterion, did not uniquely imply the validity of the relativistic Doppler equations. In fact, using an approach in line with the referenced study, it was revealed that an infinite number of frequency shift equations would satisfy the employed validation criterion. Nonetheless, it was shown that even if that claim was hypothetically accepted, then the experiment would prove nothing but a contradiction in the Special Relativity prediction. In fact, it was clearly demonstrated that the relativistic blue shift was the consequence of a time contraction, determined via the light speed postulate, leading to the relativistic Doppler formula in the case of an approaching light source. The experiment would then be confirming a relativistic time contraction. It was also shown that the classical relativity resulted in perceived time alterations leading to the classical Doppler Effect equations. The “referenced study” result could be attributed to the classical Doppler shift within 10 % difference.