The light-from-rear-going-past-car experiment and the Michelson-Morley experiment are by no means analogous. In the former, the light source is OUTSIDE the moving system. In the latter, the light source is INSIDE the moving system. So applying the principle of relativity to the light-from-rear-going-past-car experiment is incorrect and the result c'=c-u is true, as demonstrated here:

"When an observer moves away from a stationary source...the velocity of the wave relative to the observer is slower than that when it is still."

*View: http://www.youtube.com/watch?v=SC0Q6-xt-Xs*

Applying the principle of relativity to the Michelson-Morley experiment is correct because both source and observer are INSIDE the moving system. The measured speed of light will always be constant, c'=c, and the two perpendicular beams of light will always return simultaneously. This implies, however, that relative to a stationary observer OUTSIDE the moving system, the speed of light will be c'=c±v, as posited by Newton's theory (it is THIS scenario that is analogous to the light-from-rear-going-past-car experiment):

"The null result of the Michelson-Morley experiment was unhelpful and possibly counter-productive in Einstein's investigations of an emission theory of light, for the null result is predicted by an emission theory." http://philsci-archive.pitt.edu/12289/1/Einstein_Discover.pdf

"Emission theory, also called emitter theory or ballistic theory of light, was a competing theory for the special theory of relativity, explaining the results of the Michelson–Morley experiment of 1887...The name most often associated with emission theory is Isaac Newton. In his corpuscular theory Newton visualized light "corpuscles" being thrown off from hot bodies at a nominal speed of c with respect to the emitting object, and obeying the usual laws of Newtonian mechanics, and we then expect light to be moving towards us with a speed that is offset by the speed of the distant emitter (c ± v)." https://en.wikipedia.org/wiki/Emission_theory

Banesh Hoffmann, Einstein's co-author, admits that, originally ("without recourse to contracting lengths, local time, or Lorentz transformations"), the Michelson-Morley experiment was compatible with Newton's variable speed of light, c'=c±v, and incompatible with the constant speed of light, c'=c:

"Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd: A stone thrown from a speeding train can do far more damage than one thrown from a train at rest; the speed of the particle is not independent of the motion of the object emitting it. And if we take light to consist of particles and assume that these particles obey Newton's laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether." Banesh Hoffmann, Relativity and Its Roots, p.92 https://www.amazon.com/Relativity-Its-Roots-Banesh-Hoffmann/dp/0486406768