OK; I'm really curious now, so I had a look at my bike.
Long story this, so be patient.
This is a long shot, and quite bizarre, but worth a try.
First, my key only turns towards the front of the bike, but this is irrelevant here.
Not a lot is known about this, but under the rear seat itself, at the rear, is a lever (black plastic 4cmx1.5cm) that allows the seat to be angled more up at the back, to give a downward slope to the tank. It does this by pushing up the inners of the seat squab.
Next, the lever rotates on a lateral axis, and rests flat against the underside of the seat; towards the rear is standard, towards the front is sloping the seat forward.
Now, if the riders seat is taken off, and then refitted, but the lever is not in one of the two stored positions (flat against the underside of the seat), but left pointing downwards, then when the seat is installed, it may be possible for the lever to hit the bike before it should, and then fold backwards towards it's resting position.
It's also possible that it catches under a black metal crossmember on the bike on the way down.
If all these ifs coincide, the seat will look in the correct position, but will be trapped there by the lever under the crossmember.
To check out this theory:-
Remove pillion seat.
With a mirror and torch, look under the crossmember, and see if you can see this black plastic lever.
If you can, then try to push it downwards away from the crossmember, and at the same time lift the rear or the riders seat - it's a mighty strong spring though! It may not work.
If you cannot see (or feel) this lever, at least you know this isn't the cause.
Finally; yes, a photo from me would be handy, but I cannot attach one1
I really must join!