Nope, you could have an argument that I don't expect or that adequately answers the question. I'm pretty confident, yes, that what you do assumes that creatures are noticed unless there's special circumstances. Nothings you've said so far moves this needle, yet you continue to claim you don't have this starting assumption. I mean, my position is that things start by being assumed noticed and then, if circumstances are special, you look at it and make a ruling. You've locked down on saying there's no baseline assumption in play. The only way that can be true is if you're always, every single time and in every single action, evaluating the situation and applying ad hoc judgements about what's going on. It would be chaos. Yet, you seem to think that agreeing there's a baseline assumption is a gotcha questions to lock you into an agreement on how to rule things. It's not, and has never been. It's just a clear observation on how things start. It's perfectly fine if you have a different threshold for special circumstances than I do -- we can easily disagree here and I don't care. The part that's frustrating to me is that you insist that you're specially considering at all times when that's ludicrous on it's face. That you do it because you fear I'm leading you into a devious trap to gotcha you into agreeing with some other statement is just paranoid.
For me, the baseline assumption (default, if you will) is that creatures notice one another. If everything else is equal, this is what happens. If a special circumstance occurs, then I will evaluate it and make a ruling, but my bias will always be towards noticing. This is because the game sets this up by having a specific action and rules for being not noticed, so noticed must be the baseline.
Invisibility works into this as a possible source of special circumstance. I say possible because the rules in invisibility specifically call out that it enables using the hide action, but doesn't say it takes it's place. That tells me that the default assumption of noticing is still in place because invisibility increases the ability to take the baseline action to be not noticed but doesn't replace it. Still, invisibility can be a strong input to a special circumstance that makes a creature hidden without taking the specific action. Where people draw that line is up to them.
To route this back to the baseline, it's pretty clear, to me, that even you agree at some level that invisibility doesn't alter the baseline because you'd otherwise be arguing for what has to occur to be able to notice an invisible creature rather than arguing there's increased areas where an invisible creature is not noticed. The very direction and locus of your arguments shows a bias towards detection, which makes your continued evasion more frustrating. There's no trap, here, past acknowledging that there's a bias, baseline, or default assumption that creatures are noticed and it's a special circumstance that changes that and calls for a GM ruling.