You aren’t wrong, and I don’t think you’re being overly pedantic, but you also didn’t explicitly mention the distinction that most leftists draw between private property (i.e. property that is owned by someone who does not use it, but makes other people pay to do so) and personal property (property that is owned and used by the same person, like the aforementioned toothbrush). Most people who object to the original statement don’t know the difference and use the terms as if they were synonymous.