Addressing your question: "if there is a logic used in language." The idea of trivium established in the past by Greek philosophers can help explain. In the order of "grammar, logic, and rhetoric," a person would study grammar in order to use a language at the elementary level, then study logic to group sentences with correct grammar into logical syllogisms. Through the syllogisms, one can then apply rhetoric to his arguments. In this sense, there is definitely logic in the language we use, otherwise we would be speaking non-sense most of the time, and only logical by chance of luck.
Science is based on language, a superset of the language used. All logical thinking, whether it is science or everyday linguistics is based on the same logic. The key point is, the new ideas and terms that science introduce are not of the original system, and careful definition is required to understand the science, or "technical" terms used.
The way I see it, Sabine merely presented a contradiction as a rhetorical device to hook the reader's attention. She is telling the author that pointed out said contradiction in a previous tweet to not think on assumed grounds. I would expect the later parts of the book to explain the terms to clarify any contradictions.
Hopefully this is of help.
Invariant mass, rest mass, intrinsic mass, proper mass
” all mean the same thing. So, I still don't know if it is philosophically proper to use natural language to analyze physics jargon.