If it was something that someone who didn't recognize the lyrics might think was an actual threat (or included slurs that could be interpreted as hate speech) I'm not too surprised that they took it seriously. For that kind of thing, in some workplaces even a custodian emptying the bins might feel obligated to take it to management. I work in a library and we have found discarded possible-threat-of-violence notes in the trash several times; even if they can't be traced to a person they get documented just in case. And it sounds like management accepted the explanation and didn't do anything.

Like, coworker digging through your trash while you're out sick is weird, but once they found "threatening" notes I don't think it's odd that they felt like they needed to do something about it.