You can't put semantics aside. The idea of a prefered frame of reference, as used in relativity, means a frame where the laws of physics are demonstratably different from other frames. So, there are no preferred frames in relativity, as the idea of physics being the same in every frame is a postulate of Relativity.

Now, there is nothing wrong with choosing a frame where the calculations are easier. A heliocentric frame, such as the one used in your example above, makes the calculations easier, within the solar system, relative to the Sun. But, if you are going to consider the Earth-Moon system, it would make more sense to consider the view from the Earth's frame of reference, rather than a helicentric frame. Just because the choice of a frame is made to make the calculations easier does not mean, within Relativity, it's a prefered frame.

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Some try to tell me, thoughts they cannot defend,... - Moody Blues.