The party scout was correct. Passive perception does not "turn off" when you are actively searching. It only stops if you are unconscious. You always notice anything that hasn't beat your passive perception score — even if you aren't actively searching.
You can also take actions to actively search, giving you an opportunity to sense things you haven't already noticed.
For example, if your passive Wisdom (Perception) score is 15, and a monster is lurking with a Dexterity (Stealth) roll of 14, you notice them without rolling. If the monster got a 15 or higher, though, they've beaten your passive senses. Let's say that the monster has a modifier of +3 and rolled 16 on the die, for a result of 19. In this case, on your turn, you can take actions to actively search, for which the DM can call for Wisdom (Perception) rolls. If you exceed the monster's total, you've noticed it. If you get the same total or less (19, here) the situation remains the same and the monster is undetected. For that first monster — the one with a 14 total Dexterity (Stealth) check — the situation also remains the same, which is that you've already noticed them. They aren't somehow "de-noticed".
JC (at 22:16): Now, going back to passive perception... this is, as its name implies,
passive. And, it's considered to be "always on", unless you're under the effect of a condition, like the unconcious condition that says
you're not aware of your surroundings. That really... the practical
effect of that is that basically your passive perception is shut
off. Passive perception is on basically whenever you are conscious and
aware. [...]
JC (at 23:09): Because it's passive, the player does not get to say they use it. This is a... this is something that people...
Interviewer: (Laughs) I'm using my passive perception right now!
JC: Yeah, no. It's always on. That's the baseline. Now, this brings up questions, because then people are saying that, well, how
is it that when I make an active perception check, I might get a
roll that's lower? Well, you aren't... yes, that roll is lower, but
remember your passive perception is aways on. So it really
represents the floor of your perception.
Interviewer: Right. That's an important distinction, though.
JC: Yes. So if you make an active perception check and you get a number that's lower than your passive perception, all that means is
that you did a lousy job of this particular active search, but your
passive perception is still active. You're still going to notice
something that "blips" onto your passive perception radar. Really,
when you make that roll, you're really rolling to see "can I get a
higher number?" If you fail to, well, again, your passive perception score is still active. It is effectively creating that minimum.
Interviewer: The minimum. Yeah, I don't know if that's necessarily clear to a lot of dungeon masters out there, because they will be
like, well, the opposed nature of this roll means that you were
just really bad at looking, and even though the person who is
sneaking up on you only got like a five, they're able to do so.
JC: Now, many of these sorts of situations would be erased if DMs just simply remembered to use the passive perception in the
first place. Because honestly, if something's noticable by a
person's passive perception score, they should already have noticed
it. So really, the active search is trying to find something
that you haven't already noticed,
and your passive perception score represents what you have already noticed.
Best Answer
There need not be any rule that specifically says you have disadvantage.
By RAW, circumstances can impose disadvantage on any check.
I mention this because I'm going to argue that the rules justify applying disadvantage here, even if they don't overtly require it.
Heavy obscurement is strictly more obscuring than light obscurement.
This is the part you're not going to like, so let's get to it.
Both kinds of obscurement are defined largely by example, and the sets of examples are parallel: Dim light, patchy fog, and moderate foliage are lightly obscuring; darkness, opaque fog, and dense foliage are heavily obscuring. The examples clearly show that heavy obscurement is like light obscurement, only more so.
Therefore there should be no case where anything is more visible under heavy obscurement than it would be under light obscurement. Anything that you can't see in dim light, you also can't see in total darkness.
The Hiding rules say that being heavily obscured has an effect.
Finding a hidden creature involves a Perception check, so there must be some impact on the Perception check (or the Stealth check, but note this also applies to a hidden object, which likely wouldn't get a Stealth check).
The check doesn't automatically fail.
This point was made in Xirema's answer, but to restate it: detecting a creature's presence doesn't require sight and therefore doesn't always fail under blindness or heavy obscurement.
(Except when it does. A creature like a dormant gargoyle might give no signs of its presence except that you can see it, and if heavily obscured, would be truly undetectable.)
Light obscurement imposes disadvantage on detecting a creature's presence.
Perception checks that "rely on sight" have disadvantage in a lightly obscured area. (Note that the rule isn't "require sight".) Most of us could locate another person in a dark room by sound, but as a practical matter we rely on sight to do this.
Conclusion: the Perception check to locate a heavily obscured creature must be at least as hard as rolling with disadvantage, but there's no rule that it's any more difficult than that. The game mechanic that best fits in that space is to roll with disadvantage.
Finally, I think this needs to be said:
The text is not written to be used this way.
You say that you aren't interested in what the rules are intended to do, but that's essential context for reading them at all. The Player's Handbook is a handbook. It explains how to do a thing, namely, how to play the game. It is not a legal code or a set of tournament rules.
None of the rules mentioned here rigorously define their terms. In particular, the obscurement categories are specified mostly by a handful of examples. We had another question going recently about whether partial fog and dim light combined count as heavy obscurement, and the rules give us no way to answer that.
Similarly, if you're blind, you automatically fail "any ability check that requires sight", but ability checks don't say when they require sight. You have to figure that out case by case.
There are also some consequences of this situation that are far more obvious than "disadvantage on Perception checks" but aren't spelled out in the rules. For example, the Blinded condition says you can't see. This causes you to automatically fail at checks that require sight, but what about, say, reading a newspaper? There isn't a check for you to automatically fail, but still, you can't see. To grasp the implications of the rule, you have to apply logic and experience.