It's important to remember that the entire purpose of ESIGN is to "bless" the substitution of electrons for paper. If you follow ESIGN's rules, your electrons become the legal equivalent of paper. If you don't, your electrons are not a legal substitute.
Failing to handle ESIGN correctly and discontinuing paper disclosures (required by TIS, Reg. E, TIL, etc.) sets you up for class action liability and examiner citation for multiple "pattern and practice" violations (involving Regs. DD, E, Z, etc--but not ESIGN because ESIGN is optional and provides for no penalties.) Discovery of "pattern and practice" violations generally causes examiners to take three undesirable actions: lower your compliance rating, visit more often, and dig deeper.
Here's a stripped-down version of ESIGN's rule for consent, along with [my notes].
CONSENT TO ELECTRONIC RECORDS.—...if a...regulation [Reg. E, for example]...requires that information relating to a transaction or transactions...be provided or made available to a consumer in writing [such as the requirements of Section 205.4(a)], the use of an electronic record...satisfies the requirement that such information be in writing if—
(A)....
(B)....
(C) the consumer—
(i)....
(ii) consents electronically, or confirms his or her consent electronically, in a manner that reasonably demonstrates that the consumer can access information in the electronic form that will be used to provide the information that is the subject of the consent [i.e.- the disclosures required by Section 205.9(b)]....
As you describe your process, it sounds like the customer has demonstrated at least one of the necessary steps to receiving your e-documents--successful access to your Internet banking system. If IB customers must have and use Acrobat to access this system, then you've already covered the second demonstration--ability to open and use .pdf files. On the other hand, if customers are not required to have and use Acrobat for any other purpose, then you cannot fall back on a previous "test drive" as a demonstration of successful use of Acrobat. If you have not confirmed (or are uncertain) the customer's proficiency with Acrobat, you will need to set up a "test drive" so the customer can demonstrate satisfactory use of Acrobat.
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...gone fishing.