Wow... chartering a 747? That is indeed impressive - as long as they're not on the brink of bankcruptcy again, or their astronomic employee bonuses eat up their claim funds
I don't think there's much difference if at least the insurance fine-print is comprehensive enough. For most global insurances they centralize such services and have only sales offices dotted worldwide.
But you are somewhat right: I have signed up with German bank account with German address of my parents for a policy issued in Germany, but with global coverage. It wasn't so much for the point you've mentioned, but there's indeed a (small) difference in what e.g. DKV health insurance is offering to German customers and what to Expats. But the differences are openly lined out in the fine-print of the insurance policies - at least with them there is no further hidden discrimination on residency. Another good sign is that even for the Expat insurance at DKV you have to send your claims back to Germany to process - so you would assume that everything is handled there to the same standard / service level.
Maybe simply ask Chartis, Zurich and AMEX how they handle their claims. Could be that their SOS hotline number is the same as for US and Swiss-issued insurance policies, etc.