Relativity of Simultaneity - Bad Explanations on the Web

A common example used to demonstrate the Relativity of Simultaneity goes like this, more or less:

A train of length D is passing by a platform of length D. An observer P stands in the middle of the platform, and there's another observer T who sits in the middle of the train. P notices that the front end of the train coincides with the front edge of the platform AT THE SAME TIME as when the rear end of the train coincides with the rear edge of the platform. The two 'coincidence events' are thus simultaneous in P's frame of reference.

The question is, does T agree that both 'coincidence events' are simultaneous in T's frame of reference? (It is implicitly assumed that this question is posed in P's frame of reference and that both reference frames are inertial.)

The correct answer in Special Relativity is "No".

Call the front coincidence event F and the rear coincidence event R. Then, according to T, F happens before R. The events are NOT simultaneous in T's frame of reference even though they are simultaneous in P's frame of reference.

The Bad Explanation

Often times, the bad explanation for this is an incomplete version of a correct explanation provided by Einstein himself [Ein1924]. The bad explanation goes as follows: