If by "distinguished environment" you mean "the original global
environment of the Lua state created by the host program",
I almost, but not quite, agree. [2]
I was using it as defined in section 2.2 of the ref manual, which defines it to mean that very thing; whatever environment is currently at the well-known registry index; though the manual is slightly ambiguous on this point (it might mean that the distinguished environment is the ORIGINAL one in the registry, or the CURRENT one)..
[1] Binary chunks can have _ENV parameters, so (a) is possible.
Interesting, how do you do that?