It's safe to assume that the international Amex cards issued in the UK have flexible criteria.

I definitely did not need to provide a guarantee or a letter of credit, just a reference. The thing is they have customers from all around the world and they have no way to easily check your credit rating, etc. because they are a UK entity. They can't just pull your German/Swedish/whatever credit file.

So I think they have different levels of due diligence based on your history, your location, who you bank with and various other Amex risk criteria.

There's no blanket requirement for an actual bank guarantee.