Bill, riding a horse sidesaddle is a completely different thing to riding pillion on a motorcycle
Being able to grip the pommel of the saddle ( specifically designed and in some cases "tailor made" by a saddler ) between the legs
Which affords the rider a degree of control over their balance and stability
Plus being in control of the horse through the reins with both hands
Sitting sidesaddle on the back of a motorcycle, does not give the passenger any secure seat to anticipate the braking and acceleration forces which are generated as the bike makes progress along the road
Very sedate riding on smooth tarmac roads may well be possible without too much instability
But on roads which have uneven surfaces, (which many rural roads in these "third world " countries have) the passenger may well be thrown around or bounced off the seat causing problems both for them and the rider
Sandi, a scooter is a lot less stable than a bike, due having ( in most cases ) much smaller wheels which generate less "gyroscopic" force
Which is the force that keeps the machine upright and traveling in a straight line
And in answer to HF's observation
That could have been a moot point but for the fact that ( to the best of my knowledge ) it was only the Vespa which had a pronounced "offset" engine, although the Lambretta was slightly too
And they were "offset" to the left or nearside, which is the side that the passenger seems to adopt mainly when riding sidesaddle
Thereby increasing the weight on that side of the machine
Although in countries where they drive on the right
One would expect the pillion to sit with legs on the other side, away from oncoming traffic
Just my extra two pennorth
Which may or may not provoke some comments