My intial response would be "No" as well. That report indicates that the person has had issues handling an account in the past. As an executor, they are handling the estate's funds rather than their own. This means that the beneficiaries of that estate have an interest in how those funds are handled.
If the executor mishandles the funds in a way that results in NSF or other charges, then those same beneficiaries may point to that Chexsystems report as an indication that the Bank was aware of the person's problems handling an account.
They may or may not have a case, but I wouldn't want to spend the money and time defending from litigation that the bank should've taken more care with the account given that information prior to opening the account.
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The above is my opinion, and is frequently valued at USD 2ยข or less.