As I said, it's a loose definition, but the same could also be said, if I place a second computer at my parents place for example so I can have an offsite backup. They technically could also be monitoring it and have physical access. I don't think anyone would argue that this isn't self-hosting though.

For me at least self-hosting is mostly about having control of a computer/server software wise, not physically. That is probably an important differentiator from homelabbing, which is more focused on controlling the hardware. You can combine the two, but for self-hosting you don't need to physically control the hardware.