I can’t say I’ve ever heard the one about classical music making people “smarter”, but it would not surprise me if some music is simply more distracting than others. Most classical music is inoffensive enough to the ears that it’s ok to use as background noise, and the lack of lyrics doesn’t distract language processing.

What I’d be more curious about though is if there is any significant impact to quality of work during tests/study time/reading time with background noise like classical music versus just having dead silence.