Armstrong, who lives in Denver, didn't attend the meeting Friday. However, in a statement included in Zions' 2013 proxy report, he argued that when only one person serves as chairman, president and CEO, that person is accountable only to himself.
"The proponent believes that greater accountability is beneficial to good business practices and could have prevented the 2008 problems [that emerged during the financial crisis that year] which caused earnings to slide and dividends to be reduced to a penny," Armstrong said.
During the meeting, Simmons defended the board's current structure. He said the company and its top management receive "substantial oversight" from the board's 10 directors nine of whom are independent. Only Simmons, the chairman, is a bank employee.
After the meeting, James Abbott, who runs Zions' investor relations department, said there isn't compelling evidence that shareholders are better off with a chairman who isn't a company employee.
"There's no real evidence that supports this initiative; there is clear evidence that it's quite detrimental'' to a company's earnings and stock price, said Abbott, who cited a study published earlier this month in the Harvard Business Review magazine.
The notion of establishing an independent chairman became a hot topic this year when public union shareholders sought to take the chairman's duties from JP Morgan CEO Jaime Dimon. Shareholders defeated the proposal last Tuesday.
Zions' meeting was uneventful otherwise. All 10 directors were easily reelected for another one-year term.