Under KYC (Know your Customer) regulations, banks need to collect enough information to be in compliance with US law.. other countries generally have similar regulations. Here is Dow Jones' interpretation:
Customer Identification Program At the minimum, firms must pull four
pieces of identifying information about a client, including name, date
of birth, address, and identification number.
Most firms take additional steps in their screening process. Many will
make sure that clients do not appear on government sanction lists,
politically exposed person (PEP) lists, or known terrorism lists—
those who do appear usually require enhanced due diligence.
Other items considered at this time include financial transactions,
which firms use to separate potentially risky behavior from regular
business activity.
Much of this information comes from various reporting agencies, public
databases and third-party sources.
Customer Due Diligence (CDD) Customer due diligence is the process of
classifying all the information collected during the Customer
Identification Program.
Firms examine the nature and beneficiaries of existing relationships
to ensure all activity is consistent with historical customer
information.
The goal is to obtain enough information to verify a customer’s
identity and assess their riskiness. Since financial crime happens
quickly, firms frequently monitor this information for unusual spikes
in activity or changes to sanction lists. Most clients pose little to
no risk, but the few who do are subject to enhanced due diligence.
Enhanced Due Diligence (EDD) If a customer is believed to pose
additional risks, firms take extra steps to gain a better
understanding of their motivations. A high-risk person may include
those with political exposure or relationships with designated
persons. Even someone in a high-risk country can raise a red flag for
compliance.
In practice, firms must demonstrate a deeper understanding of the
high-risk clients identified by a standard customer due diligence
program. Some of the information required to perform enhanced due
diligence includes a source of wealth verification, detailed
management reports and relevant third-party research.
More prescriptive requirements can be found, for example, in Australian legislation (emphasis added):
KYC information means ‘know your customer information’ and may include
information in relation to matters such as:
(1) In relation to a customer who is an individual:
(a) the customer’s name;
(b) the customer’s residential address;
(c) the customer’s date of birth;
(d) any other name that the customer is known by;
(e) the customer’s country(ies) of citizenship;
(f) the customer’s country(ies) of residence;
(g) the customer’s occupation or business activities;
(h) the nature of the customer’s business with the reporting entity –
including:
(i) the purpose of specific transactions; or
(ii) the expected nature and level of transaction behaviour;
(i) the income or assets available to the customer;
(j) the customer’s source of funds including the origin of funds;
(k) the customer’s financial position;
(l) the beneficial ownership of the funds used by the customer with
respect to the designated services; and
(m) the beneficiaries of the transactions being facilitated by the
reporting entity on behalf of the customer including the destination
of funds.
Generally, financial institutions are conservative by nature, and a foreign-resident customer is already presenting a red flag. Less prescriptive requirements mean that they will want to collect more, not less, information.
They would much rather lose or refuse the business from many, many mid-size customers than risk the extremely punitive measures that the US government can impose on them. For a similar reason, as OP has probably found, many foreign financial institutions simply won't do business with "US Persons" because it carries great potential risks from extraterritorial application of US laws.