I think that you are missing my point.
St John's Ambulance was, at its foundation, a Christian organisation. At the time it began, church attendance in the UK was somewhere between a third and a half of the population each week. Consequently, StJA, as a Christian organisation, had a large pool of potential members, and it was straightforward for it to spread around the country.
Christianity, unlike Judaism, is an evangelical religion. Consequently, Christian missionaries were active in places like Singapore and Malawi from an early date. Organisations like StJA were a natural adjunct to those activities, and I would be very surprised to find out that there was a substantial non-Christian membership of StJA in those countries in the early days.
Its Christian origins have faded into the background now, but they remain key to its foundation and the manner in which it spread.
Hatzolah, otoh, is a Jewish organisation, and thus its chapters are likely to be concentrated in areas with large Jewish populations. Judaism is not an evangelical religion (though it does accept converts), but despite this, Hatzolah will help anyone, of any religion.
Hatzolah is just like StJA in that it will help anyone. It is like StJA in that it was founded in areas with large numbers of people that subscribe to its religious ethic. It is unlike StJA in that Jews don't missionise, and unlike StJA in that its religious ethic remains front and centre.
But it operates like StJA - for anyone who needs it. That's what is important here. That was the point I was trying to make.
And I never said that StJA only exists in Christian areas. You can't 'debunk' things that you don't read properly.