I would say at this level it’s pretty international, and I could totally see a person in one country like the USA with money to burn wanting to be owner of a horse competing at the highest levels, which in dressage would mean being based on Northern Europe.
As far as Israel, there are strong ties between some Americans and Israel. That doesn’t surprise me at all.
I expect that the ownership doesn’t matter at all until the Olympics are on the horizon, and that’s not something you necessarily anticipated 5 or 10 years ago when you started the arrangement.
As far as the human side, I know there was a Canadian dressage rider who just missed the Olympic team last time around and who then started riding under the flag of a smaller European country in Florida the following winter. I forget how she did this, maybe via her husbands nationality?
I don’t think any Canadian or American citizens are getting spots on the German, Netherlands, or British equestrian teams. The Germans have a very deep pool of talent. The FEI rankings are interesting reading. Top ranked in Canada or the USA is generally about world 100. If you didn’t make the Canadian or US team it could be a career move to take your ranking to a smaller country though ilm not sure that gets you to the Olympics necessarily.
The Olympics are the best of each country competing against each other. They are not the world top ranked riders competing against each other. For dressage, that’s going to be happening in Northern European CDI4* where you get the Germans and Dutch etc who dominate the FEI world top 20 fighting it out to pick the world top 4. Then they compete against the Canadian team which might be world 120.
Canada and the US qualify for the Olympics by competing in PanAm games against the underfunded developing countries of Central and South America. So unless they screw up and get disqualified for drugs there is always an Olympic slot.