Yes, it happened every now and then. But it was very lax. Very few videos got actually taken down. For instance, if a dancer used some music for his/her choreography, YouTube issued a warning that the music is copyrighted. I am an oriental dance teacher and a lot of such videos. Most of them have warnings, but they've been there for years now. Even unlisted videos (posted only for my students to learn the choregraphy) had that yellow mark.
Now, however, something has drastically changed. It has happened to many of my friends and colleagues. Their video gets muted (no music!) which is an utter disaster for a dance piece. Another friend of mine who used some music for background got her video muted and now it shows "not available for your country". She had to hunt for royalty-free music and have it redone to reupload it. It's a hecatombe!