Oh, no. See, at the very beginning, where he first uses the term "stationary system," he says:

Originally Posted by

**Einstein**
Let us take a system of co-ordinates in which the equations of Newtonian mechanics hold good. In order to render our presentation more precise and to distinguish this system of co-ordinates verbally from others which will be introduced hereafter, we call it the "stationary system.''

"Stationary system" does not mean "the system that an observer considers to be stationary," it just means "the specific system that I identified at the beginning." The reciprocity of SR, that either of two moving observers can be considered to be at rest, does

**not** mean that either observer can be considered to be in that specific system (named the "stationary system"). It just means that either that specific system

**or** the other system (or

**any** other system) can be considered to be at rest.