To be honest, me neither. As far as I remember, it was the result of a compromise because some people objected to the use of crossing=no for these cases because they understand that it means it is forbidden to cross.
The current wording in the wiki (without having checked when and why it was last modified) is
crossing=no: Where definitely no crossing is possible/legal. Used at places where one would expect a crossing, but where there isn’t one. As crossing=no excludes the existence of a crossing, it must be used without highway=crossing
Sentence two is what we want to indicate, but sentence one postulates that it should only used when it is not possible, which is a pretty strong wording.