I find the comments people make on YouTube around this non-understanding somewhat interesting. The "stealing" metaphor seems to have led to the unintended consequence that people are confused by what "copyright infringement" even means, thinking that maybe it only applies to something like plagiarism--- "stealing" a work by claiming that it's yours when it was actually made by someone else.
So the solution is to still post the video, but with a confusing disclaimer like, "this video isn't mine, all music belongs to [artist], no copyright infringement intended". Saying "no copyright infringement intended" while still uploading the video is strange thing to be doing, unless you have a nonstandard understanding of what copyright infringement means.