According to PHB p. 189:
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.
Thus the process of the DM determining who might be surprised is:
- If neither side is 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.
So I take this to mean there is always a check of some sort.
The scenarios listed still fall under this process:
Adventures go in a cave and clear it out (multiple encounters). On the way out some goblins "Hide" outside the cave with total cover (awaiting for the adventurers to come out and ambush them). Scout leads the way and is surprised.
This scenario should still have a stealth-goblins vs perception-scout check even if the scout didnt say he was actively looking for hidden creatures (use his passive). If you cannot see the hidden creatures, you still have a chance to hear them. This is based off the DMG p.243
Outdoor visibility can be hampered by terrain, weather, and time of day. Creatures can be more likely to hear one another before they see anything. If neither side is being stealthy, creatures automatically notice each other once they are within sight or hearing range of one another. Otherwise, compare the Dexterity (Stealth) check results of the creatures in the group that is hiding with the passive Wisdom (Perception) scores of the other group, as explained in the Player's Handbook.
Adventures come up and see a dead body on the floor (see statues on the sides of the room, see motionless skeletal bodies scattered about the room). The scout approaches and is attacked as the undead/statue seemingly comes to "life".
Here neither party is in stealth and they both notice each other. Despite the creature being motionless, the scout should not be surprised that it attacked. You are already in a dangerous area and are already on high alert (a dead body/skeletons/statues in a cave/dungeon is not normal). Plus the scout was approaching to investigate further. In any case the rule states if neither side is stealthy, they automatically notice each other - thus no surprise. OR, give the scout a perception check to see if he notices something about the creature as he approached/looks at them (failure of the check may mean surprise).
Jack and Jill go up a hill to fetch a pail of water. Jill pulls out a knife and stabs Jack.
In the real world, Jack would be surprised that his friend stabbed him. However this is DnD, neither side is stealthy, they automatically notice each other - thus no surprise. Or there could be a check to see if Jack notices Jill pulling out a dagger and lunging at him with it (failure to notice/act quickly enough may give Jill a surprise round).
Surprise should not just happen, there should be a check of some sort or there is no surprise round. When the "DM determines who might be surprised" he is doing the appropriate/required checks (passive or active) for each of the parties and letting everyone know if there is a surprise round and who can act.