Crisis, you left out some more quotes:
“Compared to most other European folk music styles, little is known about the history of klezmer music, and much of what is said about it must be seen as conjecture.[2]”
“Klezmer is easily identifiable by its characteristic expressive melodies, reminiscent of the human voice, complete with laughing and weeping. This is not a coincidence; the style is meant to imitate khazone and paraliturgical singing. A number of dreydlekh (a Yiddish word for musical ornaments), such as krekhts (“sobs”) are used to produce this style.”
So sure, the klezmorim fused other types of music into the traditional style, but at its heart, it’s Jewish.
Compare that to today’s popular “Jewish” music, which is 90% derivative.
You’re also unfairly comparing older European non Jewish styles to rock, although they’re very different.