I think it's a pretty clear line. Self hosted means you can run it locally in your home, using a saas platform or vps is just a convenience, not a requirement.
I hope AI will push infra, including good-enough AI itself, dirt cheap, so that everyone has "good enough" software for themselves. Tailscale is a game changer in this regard but only the first step.
This is probably considerably less true in countries with a smaller ip to population ratio e.g. india.
the complaint is the communication, not the literal words. because the title conflicts with itself, it causes confusion.
for example, saying, "come join us. I'm hosting a dinner party. It's at this restaurant," would be similar.
It's perfectly reasonable and understandable to say you're hosting the party even if you don't own the physical location (see also: weddings)