IANAL, but you should consider the relevant state and federal documents to determine whether "financial transactions" would pass the test of "doing business". A good example of a how New York determines how it defines foreign corporation "doing business" is here.
However there are some differences of opinions regarding taxation: from delawarecorp.com (not the state site):
Citizens of countries other than the United States are often concerned
with the tax consequences of owning an entity such as a limited
liability company. A Delaware LLC that (1) carries on no business in
the U.S., (2) derives no income from any sources within the U.S. and
(3) has not elected to be treated for tax purposes as a corporation
does not need to file a U.S. tax return or a Delaware tax return.
Under the current IRS "check-the-box" rules, a Delaware LLC that does
not affirmatively elect to be treated for tax purposes as a
corporation will be treated for federal tax purposes as a partnership.
It will be treated as a partnership for Delaware tax purposes as well.
Under current Treasury Regulations, a partnership that carries on no
business in the U.S. and derives no income from any source within the
U.S. does not need to file a tax return. Delaware law currently
provides that a partnership need file a return only if it has income
from sources within the State of Delaware.
If the LLC has only one member, then for federal tax purposes the LLC
is disregarded, and the sole member is taxed as a sole proprietor.
Current Treasury Regulations provide that a nonresident alien who is
not engaged in a U.S. business and who does not derive any income from
any source within the U.S. does not have to file a tax return.
Similarly, Delaware law currently provides that a nonresident alien
having no income from sources within the State of Delaware does not
have to file a Delaware return.
I don't quite know how one would be able to accept payments in the US from US companies and and assert that the company "derives no income from any sources in the US."
That said, I wouldn't trust anyone's opinion on this matter except your lawyer.