It is my understanding that a sign disclosing transaction fees does not have to be posted at each of the bank's ATMs as long as the applicable ATM transaction fee is disclosed on the screen, and the consumer has the opportunity to cancel the transaction if they do not want to pay the fee. Is this correct?

From REG E (a sign on the machine as well as on the screen before a fee is charged would be required)

§ 205.16 Disclosures at automated teller machines.

(a) Definition. Automated teller machine operator means any person that operates an automated teller machine at which a consumer initiates an electronic fund transfer or a balance inquiry and that does not hold the account to or from which the transfer is made, or about which an inquiry is made.
(b) General. An automated teller machine operator that imposes a fee on a consumer for initiating an electronic fund transfer or a balance inquiry shall:
(1) Provide notice that a fee will be imposed for providing electronic fund transfer services or a balance inquiry; and
(2) Disclose the amount of the fee.
(c) Notice requirement. An automated teller machine operator must comply with the following:
(1) On the machine. Post the notice required by paragraph (b)(1) of this section in a prominent and conspicuous location on or at the automated teller machine; and
(2) Screen or paper notice. Provide the notice required by paragraphs (b)(1) and (b)(2) of this section either by showing it on the screen of the automated teller machine or by providing it on paper, before the consumer is committed to paying a fee.
(d) Temporary exemption. Through December 31, 2004, the notice requirement in paragraph (c)(2) of this section does not apply to any automated teller machine that lacks the technical capability to provide such information.
(e) Imposition of fee. An automated teller machine operator may impose a fee on a consumer for initiating an electronic fund transfer or a balance inquiry only if
(1) The consumer is provided the notices required under paragraph (c) of this section, and
(2) The consumer elects to continue the transaction or inquiry after receiving such notices.

There was an exception that delayed the dual requirements ((c)(2) above) but that expired a year ago. Perhaps someone hasn't updated their records or policy.

Short answer - There are two notices required if you assess an ATM fee to cardholders of other banks. The first is a notice on or at the machine, which does not have to indicate the amount of the fee. The second is a notice on the screen or a printed notice, that includes the fee, and tells the user how to bail out of the transaction without incurring the fee.