It's hard to prove non-existence, but there is no evidence of there being a legal requirement on the Agent to provide personal financial information to a third party. Taking RCW 11.125.200 as a starting point,
(1) Except as otherwise provided in subsection (2) of this section:
(a) A person shall either accept an acknowledged power of attorney or
request a certification or a translation no later than seven business
days after presentation of the power of attorney for acceptance...
(c) A person may not require an additional or different form of power
of attorney for authority granted in the power of attorney presented.
"Shall" means that they must accept it, end of discussion. Subsection (2) say when they don't have to accept the form:
(2) A person is not required to accept an acknowledged power of
attorney if: (a) The person is not otherwise required to engage in a
transaction with the principal in the same circumstances; (b) Engaging
in a transaction with the agent or the principal in the same
circumstances would be inconsistent with federal law; (c) The person
has actual knowledge of the termination of the agent's authority or of
the power of attorney before exercise of the power; (d) A request for
a certification or a translation is refused; (e) The person in good
faith believes that the power is not valid or that the agent does not
have the authority to perform the act requested, whether or not a
certification or a translation has been requested or provided; or (f)
The person makes, or has actual knowledge that another person has
made, a report to the department of social and health services stating
a good faith belief that the principal may be subject to physical or
financial abuse, neglect, exploitation, or abandonment by the agent or
a person acting for or with the agent.
none of which arises in the situation you describe. This law (the Uniform Power of Attorney Act) exists in most states. New Jersey law has somewhat different conditions on acceptance, that
Any third party may rely upon the authority granted in a durable power
of attorney until the third party has received actual notice of the
revocation of the power of attorney, the termination or suspension of
the authority of the attorney-in-fact, or the death of the principal
but there is no clause saying "only if the agent provides personal financial information".
It may be necessary to get a court order to force a party to accept a valid POA, especially if the state hasn't enacted the Uniform Power of Attorney Act.