By the rules, you are 100% correct on both counts. Whether or not that is "realistic" or should be true in the "real world" is a different question. (I put "realistic" and "real world" in quotes because we don't have a real-world example of invisibility to use an example).
I think that part of the issue is that (to paraphrase The Princess Bride), as used in the D&D rules, the word "invisible" does not mean what people typically think that it means. Based on the common use of the word and the way invisibility is typically depicted in fiction, I agree that detection of the invisible person in both scenarios above would not be possible and would not be "realistic". The fact that the rules allow for detection of the invisible person under both scenarios means that the D&D rules do not use the words "invisible" and "invisibility" the same way that we use them in normal life. Now, that may be problem with the way the rules are written, maybe the rules should do a better job of explaining what invisibility actual is, should better explain how something that is invisible "looks" or can be detected, etc., but those are ultimately different issues from how invisibility operates within the rules.
I think that the designers deliberately chose to make invisibility "unrealistic" in order to avoid invisibility effects from becoming too powerful and to keep invisibility from largely negating or swallowing the stealth skill. I think part of the reason there is such "debate" over how hiding, invisibility, etc. work is the designers did a poor job of making it clear that, again, as used in the D&D rules, invisibility does not mean what most people think that word means.
As an aside, one thing I always try to keep in mind when interpreting rules is not no "reify the flavor text" or the word used to describe a condition. For example, I think there is also a disconnect between what the D&D rules mean when they say "paralyzed" and what people mean when they say "paralyzed" in real life. In day to day life, people think of someone who is paralyzed as someone who cannot move at all, cannot offer any resistance to a melee attack, and, for example, whose throat you could leisurely slit (i.e. auto kill). The fact that, within the D&D rules, you cannot auto-kill someone who is paralyzed means that when the rules say "paralyzed" they do not mean someone who is "paralyzed" as we use that word in our day-to-day life. Because you cannot, by the rules, auto-kill someone who is paralyzed, in the D&D rules, paralyzed means someone who is at a disadvantage but who can still move enough to somewhat defend themselves from a physical attack. Now, the rules could do a better job of explaining the above and maybe some conditions should not be described with the words that are used to describe them, but, that is also a different question.
For my group, despite the disconnect with the fiction and the fact that it is "unrealistic", we go with the rules as written precisely because we think that the rules properly "rein in" invisibility and keep it from dominating the game. To justify it in ours minds, we throw out a post-hoc "Predator-shimmering-effect" description to harmonize the rules with what the PCs, NPCs, monsters, etc. "see". That works for us.
