Sunshine Adagio In D Minor HOT!

The tracks "Sunshine (Adagio in D Minor)", and "Kaneda's Death Pt. 2 (Adagio in D Minor)" have been adapted in other media. Variations of the adagio's progression appear in many films, television programs, trailers, and adverts. Notably, John Murphy heavily re-used the adagio as a theme during composition of the Kick-Ass soundtrack, and wrote a series of variations for use in the film. Other examples include:

Sunshine Adagio in D Minor

My rudimentary analysis tells me this mainly uses a very straight forward progression of I vi iii V (and a little bit of variation) in Em. But why would it be called "Adagio in D minor" then? I mean, is there something I'm overlooking, from a theoretical POV?

Other people on web pages like _in_d_minor_john_murphy_but_why_d_minor/ that ask the same question often assume that this answer means that the original, unpublished piece was in D minor and the film version is in E minor.