Should (must?) bank signatures be true?

How important is it that signature cards on file with a financial institution be true and correct?

What happens if they are not?

"Every transaction between a financial institution and a customer—from depositing a check to applying for a home loan to one company acquiring another—relies on one document: the signature card. Without this simple but crucial document, all parties to any financial transaction would be at greater risk of fraud." Source: docusign

That "all parties" part ought to worry some of the folks on the Board of the HOA. 

Because many signature cards can now be e-signed, is it easier to sit at home and lie, instead of going into the bank and lying to a bank manager? 

Just exactly where is the problem for the officers of the HOA? 

When one of them signs as President and another signs as Treasurer, the financial institution (banks or Edward Jones) believes them.

The problem is that they are not the legitimate officers of the HOA. They were not "duly-elected" by people who were eligible to vote for them. That's because the Directors themselves are not legitimate, because they were not duly-elected by people eligible to vote for them.

Without enough legitimate Voting Members, nothing else that follows is legal.

This problem has existed for years in The Summit's HOA.

What are the penalties for holding one's self out as an officer of a corporation, when that person really is not? In this case is it a Federal offense?

What would the HOA's attorney say, if he knew this was happening?

What would a bank's Compliance Officer say, if he knew this was happening?

Would he worry that the Federal regulators might look closely, if tipped off?

Why won't the HOA just straighten up and comply with its own By-Laws when electing Voting Members, Directors, and Officers?