Is this the case even if the person has CDs of the music? I can understand some artists not permitting streaming of the Apple Music owned version of the tracks (to encourage people to buy them) but how is this different from, say, if the person had a CD that was not in Apple's collection? Is this a case of there is a Match but because there is, and the Apple copy is not permitted for streaming, even the person's own CD isn't? That sounds pretty unfair to me since in theory Apple is supposed to let you upload and use the Music service to play any music you own. At least this is how I interpret your post.
By the way, I can think of at least one very easy workaround to this if it is the case. Rename your music. BBeatles, or Beetles.