Some dictionaries stick in that "unlawful" stuff into their definitions, but others don't, or give that as an examnple of where the term might be appropriate.

In fact I can think of plenty of perfectly lawful activities where the term can be used - covering up for some dodgy but legal activity of a friend, for example. Or even organising a surprise party, though perhaps that's an atypical example.

But generally if you are engaged in something you'd rather other people didn't knowm about I think the term is appropriate, even when it ain't actually illegal, I think the term is appropriate.

And when it comes to terrorist atrocities, or assassinations (leaving aside the theoretical case where just one person is entirely responsible), by definition a conspiracy of some sort has to be involved, or they wouldn't happen in the first place. So it's absurd to talk as if theories about conspiracies were always nonsense. A whole host of conspiracy theories are nonsense, but that's a different matter.

And sometimes high authorities do in fact organise conspiracies, and it's a long time before the truth comes out - for example the Gulf of Tonkin incident