> Your house isn't yours unless and until it's paid off.
That depends what you mean. It's my understanding (as a non-homeowner of any stripe) that you can do more substantial remodelling projects without asking for your landlord's blessing in a home you have a mortgage on, which seems to have been the kind of thing the parent was talking about, and is a potentially substantial practical difference in whether a space is "mine" or "not mine" whatever the actual equity situation is.
That depends what you mean. It's my understanding (as a non-homeowner of any stripe) that you can do more substantial remodelling projects without asking for your landlord's blessing in a home you have a mortgage on, which seems to have been the kind of thing the parent was talking about, and is a potentially substantial practical difference in whether a space is "mine" or "not mine" whatever the actual equity situation is.