My thoughts don't happen to other people so why are they 'not mine'? Considering the five aggregates and the sense in which they are all not-self. Thoughts (samskāra) are one of the five aggregates so they too are 'not me' or 'not mine'. In one sense this is a statement which accords with my own experience while on and off the meditation cushion. They display an impermanence and often they arising unbidden (or as part of a web of causal relationships that I don't control). In another sense however this doesn't accord with my experience. My thoughts don't happen to anyone else. They are thoughts in my head happening to me. 

I know (well I think I know) the second statement is a wrong view. So why are thoughts not mine if they never happen to other people.
When speaking in conventional terms, i.e. "my, mine, they, others, people etc." we are dealing with conventional reality. Here concepts such as "a man, woman, an animal, a Self" etc. exist.

When instead we turn to ultimate reality we realize that there is no such thing as concepts. They are not findable in ultimate reality. They have no real point of reference. We realize that the question arose out of having wrong view, as you also mention.

The reason why "your" thoughts do not happen to "other people" is because they are concepts. 

If we instead construct the sentence in another way it might make more sense. The new sentence could be: 

Thoughts arise and cease. Mental formations arise and cease. They do not belong to anyone or anything. That is a mental formation itself and it itself is impermanent, unsatisfactory and not-self. There is no thinker behind the thought. There is no "owner" of phenomena. There is no experiencing entity. There are just physical and mental phenomena arising and ceasing.

I hope this shed some light onto it. If i may give an advice from personal practice, then do not think too much about these things. Instead keep doing insight meditation as you also mention you do. The experiental knowledge you gain will cast away all illusions and concepts and lay bare the true nature of reality. 

Lastly, i would like to point you to this dhamma talk by Ajahn Punnadhammo. Its called "Anatta". Very good talk. 

I have attached a picture to illustrate what happens when we are "trapped" in conventional reality. The bottom of the picture is when one is without insight knowledge into the 3 signs of existence and thereby thinking one has a Self. When one begins practicing the path and gains insights then the breaking away of illusions and concepts happen like in the top of the picture. We become free from wrong view and gain right view.