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 
