The question can be summarized in the following aspects:

a) the popular music of the 19th century (inheritance from Renaissance
and industrial society) has as base the tempo of waltz or of march.
In the 20th century the expansion of the knowledge of the music of the
Oriental Europe, Africa, Amerindians, Arabians, Asiatic, India, Oriental
Music and of the cultures of Pacific, broken the "square rhythm" European.

b) the notation of the popular music is very precarious and superficial;
who writes it is usually an erudite that is loaded of European tradition;
then he scores - sometimes - adapting the writing and he "changes" the
music (see the Liszt registers of the gypsies' music; Bartok' registers
are authentic)

c) the computer programs don't also give all the nuances of the traditional
rhythmic, and it is still more difficult to capture the music of another
culture and also of the contemporary music

d) the popular, folkloric and tribal musicians have something that
in Brazil we called "metrica derramada" (literally:  "spilled metric"
or "loose, relaxed metric").  It is a unconscious/emotional free
interpretation (this is applied to the jazz, rock, tango etc.) of the
rhythm, speed, attack, articulation, emphasis, and other subtileness
musical nuances almost impossible of writing and one music can be reduced
in 4/4 or 3/4, but when hearing it we listened "another" music.  For this
reason the problem of erudite interpreters stumbled in a "simple music".
Myself transformed the "Titanic" in a lullaby!

Edson Ortolan
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http://sites.uol.com.br/eortolan