It is worth noting that a wrong folkoric definition of an Inertial Frame in the Popular Science literature (even in text books) reads that 'it is a frame in uniform motion'. We know very well by now that the idea of motion requires a frame of reference, so that such a definition of an Inertial Frame has no meaning whatsoever, confusing the reader because it tacitly reaffirms the idea of absolute motion -- when the goal of every didactic exposition of Relativity Theory should be precisely the opposite.
The difference between Lorentz's Transformation in Lorentz's theory and Lorentz's Transformation in Einstein's Special Relativity is not mathematical but ontological and epistemological and, being so, it was to be expected the emergence of historians, scientists, and philosophers that, not having understood in depth the philosophical content and transcendence of the theory, would minimize Einstein's contribution.
Teaching the layperson (divulgare) is not distorting (tergiversare) the subject, but educating the public; and it is our duty as scientists to educate without distorting the essence of the scientific knowledge attained by humanity. The future of our society depends upon this premise.
After some cogitation, it is difficult not to agree with Herman Bondi (1919 - 2005), who in his book 'Relativity and Common Sense' says:... The surprising thing, surely, is that molecules in a gas behave so much as billiard balls, not that electrons behave so little like billiard balls.
Einstein's theory, experimentally corroborated for the last hundred years, regardless of how outlandish and opposed to our prejudices (disguised as they are with the 'common sense' costume), is rational, consistent, and intelligible to the layperson - if s/he has the audacity of accepting the unfounded nature of those prejudices.
As we already pointed out, 'special' means 'restricted to Inertial Frames of Reference', i.e. this theory cannot describe the Universe from an arbitrary reference frame. This restricted scope is not to be ignored, though not overemphasized either. ...Ironically, and precisely because of the great success of this simple version of Relativity Theory, most of its detractors have chosen to ignore (out of ignorance or malice -- you judge case by case) its philosophical foundation and restriction to Inertial Frames, so as to declare it invalid.