When there is a monarchy, every territory that is part of their kingdom is under their control and subject to their will, period. That is how monarchies and oligarchies have always worked. A queen is, by definition, inherently a monarch. So even if “Winterfell is yours” as spoken by Sansa in the moment is symbolic welcome instead of literal like you are claiming, symbolic relinquishment of control is still relinquishment of control. In the grand scheme of things, there will be no functional distinction. Or else what would even be the point? Why even make the North kneel? Saying “the Starks dont’ control the North but it’s still their’s” doesn’t really make sense. How is it theirs if their ownership of it is still subject to the power of another? That’s more like renting, not buying; they have a lease, not a mortgage.
They don’t say this to every visitor who shows up at Winterfell, it’s not a standard greeting. I’m pretty sure it doesn’t play on their answering machine and isn’t printed on their Christmas card. There is nothing to imply Ned means “the North is yours… but not really lol.” I’m not entirely sure where you are getting that interpretation from or what you are basing it on, but I don’t see any evidence for it. Not in the actual words spoken or any other subtext. Again, that is the entire function of monarchies and how they have always operated. If it wasn’t why have them? Like, I’m sorry, but that’s just a really strange, and honestly pretty patronizing, retcon of the practice of monarchical power and I don’t quite know where you’re getting it from.