In fairness I suppose that depends on exactly what is meant by sitting "next" to them.
Sorry if my definition wasn't tight enough here - but its really a bit of a weak objection with regard to the bigger picture I would have thought.
However, I'll be a bit more specific bit for you....
Being seated in sufficient proximity to engage in conversation, should it be felt appropriate (as it apparently is by default where you come from) is different from imposing yourself uneccesarily on anothers personal space - ie sitting right next to them on the same bench, which is what I meant when I said you normally wouldn't do so in an otherwise empty carriage. To me this would simply be strange behaviour - unless I knew the person.
I might seat myself diagonally opposite or something like that in an otherwise empty carriage in a train I suppose, in order to be friendly but not intrusive, but sometimes I might not even bother to do that - no two situations are the same. Anyone who has lived in many of the widely varying regions of the country will recognise the strange but undeniable phonomenon that any rules of social ettiquette which could apply to such a situation are in any case very fluid and change according to whether you are in a conurbation or in the sticks, north or south etc.
In the village where I grew up it is polite to say hello to anyone who passes. In the town where I live a friendly smile or nod would be considered more than enough. In the city where I work people ignore each other, and anyone who is not known to you would look at you as if you were mad if you smiled, nodded or said hello to them in the street.
Getting back to the train, as you rightly point out, the same would broadly apply to the way you treat adults or children, although I'm not sure I would say so in such absolute terms - I probably treat children with kid gloves
in comparison, thereby respecting the fact that they are children. I'd afford them the priviledge of deciding whether to initiate a conversation for example, otherwise I'd leave them in peace.
If they did so in a rude or annoying fashion, I'd indicate to them that I'd rather be left in peace, ignore them, or possibly move elsewhere if that didn't work, much as I would with an adult.
Whereas I might consider it appropriate that I should introduce myself to an Air Cadet in the uniform of my old squadron, I think that this would probably not be the case with regard to a young lady in a school uniform.
Striking up a conversation with someone who happens to be seated right next to you on a crowded train is of course an entirely different matter.
Accusations of paranoia are a bit OTT in this context BTW - what about modesty, shyness, recognising body language like crossed arms and looking out the window, not particularly liking the look of someone, respecting anothers privacy, wanting some time alone while you have the opportunity, just not being in the right mood etc,etc...
Have you never reluctantly and yet politely acceded to the company of a fellow traveller who foisted himself upon you and wished to God you hadn't?
Do you ever consider that you might have unwittingly done the same to another?
Could that have been a child?
And if any of this makes it a sad world - don't blame me!