Like all sandboxes, it is an illusion. They are no different than linear adventures. The only difference is someone wanted to make a name for their supposed playstyle.
No offense to anyone. I mean that sincerely. But we are all kidding ourselves.
I take offence a little (only reason it is only a little is the example you are siteing and use below are not my style)
This above example is a perfect example:
DM: Want to deal with orc raiders?
Players: No.
DM: Well I will make you deal with them by having them wreak havoc on your campaign.
Players: Not interested.
DM: Oh yea! What about now. Now you have to deal with them or lose your homebase!
this DOES seem rails to me... if the PCs are not interested once I may escalate a little to see if they bite a second time (but I would let them do at least 2-3 things inbetween) but if they choose not to take the 2nd one I will assume they are not interested and have that plot hook eaten by either other adventures or a different plot.
back in 4e I had a NPC group of Dragon hunters and an NPC group of all arcane classes in the same campaign world and the PCs would hear of there exploits mixed in with there own from time to time... but in an early 5e campaign I had adventurers be rare so I had to have a new villian appear... (Wow, you ignored the orcs twice but a necromancer didn't where there were orcs are now ghouls and wights...) I ALWAYS follow the player lead, even if that means needing to adjust on the fly.
Sometimes (in less direct threat examples) this will mean a plot just sit unexplored... no one EVER went into that cave, or those strange lights went away but no one knows what they are...
Or...
DM: The Captain of the Guards has asked you to scout an orc threat which is camping right next to one of the outer villages under his protection.
Players: We tell the captain we can't as there are some ruins we wanted to explore.
DM: It turns out those ruins are right next to the orc encampment. Perhaps kill two birds with one stone?
Players: No. That might be too dangerous.
DM: OK. (Players show up and the orcs are also investigating the ruins.)
ugh where that COULD be fun once or twice (hey they forshadowed the orcs right) I would be pissed at a DM claiming a sandbox that pulled that in any regular rate.
Many would consider one sandboxing and the other railroading. But in reality, they are the same - playing.
okay, but try this one out...
hook 1) the captain of the guard asks you to scout the orcs in the south east
hook 2) rummor has it the earthquake last week unearthed some ruins to the south
hook 3) there is a caravan leaving to go east in 9 days and they are looking for guards
hook 4) the town cleric is acting weird
hook 5) a local thieves guild member has fallen in love with the daughter of the captain of the town guard and he has told her she is not allowed to see him (she thought him cute UNTIL her dad said no way and that made it way hotter)
PCs talk all this over and decide that the town to the north has a cool name, so they ask the DM what they know about it... the DM tells them it is a Magocracy with a counsel of wizards as the ruler and it is actually part of a tri city alliance with 2 cities farther north. One PC asks "is it only arcane magic that rules there?" the DM says "There are clerics but they are not part of the government" a diffrent PC says "Lets go see if we can get work there and they can pay us in new spells" and they head north.
when they get to the mageocracy they find that anyone without magic is treated as a 3rd class citazen, but most of the merchents and nobles know at least a cantrip or two... but the DM still has time to drop some hints to hooks
hook B1) the local blacksmith isn't really a caster but uses slight of hand tricks to keep up appearances... he is part of a resistance that wants equality
hook B2) 2 local children have gone missing... the town guard doesn't care since they are from non magical families
hook B3-B5) there is a hireing board with 3 diffrent jobs listed on it... all are going to a place to get something for a wizard family
The PCs can choose to go back to town A, do a hook from town B, or leave and go somewhere else. each town has 2-3 hooks like this in broad notes and the DM fleshes out based on what PCs do and show intrest in. there are 9 other cities (C-K) listed on the map but they also know that there are at least 2 cities north of the map part of an alliance with this mageocracy.
And I get it. If you are going to do an entire campaign impromptu, use theater of the mind, or take breaks so you can draw up maps on the fly, have to look at player notes to see what you said one month ago, always let your players just go wherever they want without any nudging, and just use random tables - then maybe you are doing something different. But, in my experience, I have never seen it - even with the most adamant "sandbox" DMs.
I'm sorry you never saw it... I have gotten WAY more sandboxey since 4e started, and I was heading this way by the end of 3.5. I don't ALWAYS do it though, and sometimes I do it to different degrees.