Question: why does it matter? I see no practical difference between your approach and
@Oofta's. At both of your tables it's ultimately up to the DM to determine whether the invisible creature's square is known, based on the DM's evaluation of how hard it would be to locate the invisible creature. You're using that evaluation to determine whether to deviate from a default, and
@Oofta is using that evaluation to determine the answer directly. Why is that difference important? It doesn't even tell us at whose table it would be easier to locate invisible creatures.
(Yes, we know from the discussion that it's on-average harder to locate invisible creatures at
@Oofta's table than it is at yours. But that isn't a necessary consequence of the difference in your approaches. It would be entirely possible for a different DM that follows your approach to decide to deviate from the "default" in more circumstances than
@Oofta would determine that the creature's square is unknown.)
To make a mathematical analogy, you're saying that x is 10, unless changed at changed at the discretion of the DM.
@Oofta is saying that is x is set at the discretion of the DM. The difference in the value of x at your tables depends entirely on how you each exercise that discretion, and does not depend on the difference in approach.