I agree with you. But actually, I think when the rules talking about "noticing a threat" in combat that it is meant to also refer to non-threatening allies. In the Hiding side-box PHB p. 177 it says : "In combat, most creatures stay alert for signs of danger all around, so if you come out of hiding and approach a creature, it usually sees you." (emphasis added).
So I believe that all cases where the wording "noticing a threat" is used in the rules, it's meant to mean that opponents "notice a threat" and allies just "notice." I'll think about making that more explicit, but I haven't heard from any players who found that ambiguous as yet.
So, you don't notice a threat if you don't think the creature is threatening.
Or, to be very, very clear: there simply being non-hidden creatures near you
doesn't make you immune to surprise.
Those non-hidden creatures can be your allies, neutral parties you don't think are going to be fighting you. If they are creatures you suspect are about to attack you, they do make you immune to surprise.
An assassin masquerading as a member of an orchestra can't surprise because they aren't hidden.
You have surprise backwards. Assassin's don't
surprise, it is the
other side that is surprised.
If they did not notice a threat, they are surprised.
So we have alice and bob, both assassins.
Alice is hiding, invisible. Bob is disguised as a member of the orchestra, and has Truesight up, so can see Alice. Bob's disguise is perfect, and Charlie has no idea that Bob is an assassin.
We have charlie, their victim. Alice starts combat.
Is Charlie immune to surprise?
Bob is clearly not surprised. Bob can see Alice. Bob can see charlie.
Charlie cannot see Alice. Bob has successfully disguised himself, so does not appear to be a threat.
Does the fact that Bob is disguised suddenly prevent Charlie from being surprised? If Bob does nothing, can Charlie be surprised? If initiative goes Alice, Charlie, Bob, and Bob hasn't acted, is Charlie surprised on his turn? If Bob then acts, does Charlie retroactively get to act?
Does removing Bob suddenly make Charlie surprised?!
If Bob wins initiative, and attacks, does Charlie suddenly become not-surprised?
Can I initiate surprise by deceiving an adjacent opponent into believing I'm actually an ally and then suddenly attacking? No, since surprise requires hiding and you would not be hidden from your opponent because they could notice that your attack was coming. This would be an initiative roll, but if your opponent who had been successfully deceived previously (Insight vs Deception check) wins initiative, they may choose to do nothing to counter your attack on their turn if they momentarily believe the initiation of your action is due to something else other than commencing an attack.
Surprise is not something you do.
Surprise is something that happens to you.
If you notice a threat (a potentially hostile person) and are ready for combat, you aren't surprised. If you don't notice a threat, and combat starts, you are surprised.
The easiest way for someone to "not notice a threat" is for that threat to be hidden. But that isn't the only way.
The existence of a 5th column spy in the PC's party doesn't suddenly make them immune to surprise from ambusing enemies. And those ambushing enemies do not suddenly make the 5th column spy more surprising.
The DM determines who might be surprised. If neither side tries to be stealthy, they automatically notice each other. Otherwise, the DM compares the Dexterity (
Stealth) checks
of anyone hiding with the passive Wisdom (
Perception) score of each creature on the opposing side. Any character or monster that doesn’t
notice a threat is surprised at the start of the encounter.
Bob, disguised as a member of the orchestra, is not a
threat that Charlie
notices.
Charlie notices Bob, as an orchestra player, but not that Bob is a threat.
So Bob's existence does not prevent Charlie from being surprised.
From this, combat starts with Charlie
surprised.
Bob gets to roll initiative like everyone else, RAW. Combat has already started, so what Bob does does not change if Charlie is surprised.
To
notice someone is not the same as
notice a threat: the rules use different terms, and the word
threat matters. You notice the other PCs, you notice the orchestra players. Noticing a threat means you have to both notice someone, and realize they are a threat.
A successful disguise (as something appropriate) or deception of peaceful intentions makes someone not a threat.