The FATCA questionnaire has absolutely nothing to do with the anti-money laundering and counter-terrorist financing questionnaire.
Just so we’re all clear once and for all, the FinCEN questionnaire isn't strictly defined by statute—in fact, no specific form is—but rather by the Hub based on guidelines issued by FinCEN.
A few relevant sections from the law:
Customer Due Diligence Measures
Section 8.
(1) Unless otherwise provided by this Act, customer due diligence includes the following measures:
1. identifying the customer and verifying their identity based on documents, data, or information obtained from a reliable, dependable, and independent source,
2. identifying and verifying the identity of the customer's beneficial owner,
3. collecting data regarding the purpose and intended nature of the business relationship or transaction, along with other data required under this Act,,
...
Data Collection
Section 25.
(1) As part of customer due diligence, when establishing a business relationship under Section 9, subsection 1, point 1 of this Act, the obligated entity collects data pursuant to Section 16. subsection 1, points 1, 4, 5, 7. and 8 of this Act.
...
Obtaining Data by Obligated Entities
Section 16.
...
7. data concerning the purpose and intended nature of the business relationship, including information about the customer's business activities;;
...
Section 7.
...
(2) The obligated entity is required to conduct a risk analysis and, using that analysis, determine the risk rating for a specific group or type of customer, business relationship, product, or transaction relative to potential abuses related to money laundering or terrorist financing.
So, look, just basic identifiers (name, address, SSN, place of birth...) aren't nearly enough for due diligence or for categorizing a client into a risk group; you also need additional data regarding the intended purpose and nature of the business relationship.
That is exactly what this Questionnaire is for:
I don't know about other banks, but at Chase, the questionnaire covers exclusively this type of data.
Obviously, you can always refuse to give the bank the information they ask for, but they can refuse to open an account or unilaterally terminate the business relationship with the client (and they probably will).
Refusal of Business Relationships and Transactions
Section 13.
(1) An obligated entity that cannot carry out the measures set forth in Section 8, subsection 1, points 1, 2, and 3 of this Act, shall not establish a business relationship or execute a transaction, specifically...is forced to terminate an existing business relationship.