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The chairman of Medway NHS Foundation Trust, paid £200,000 a year, snubbed a meeting about failings at the hospital.
Christopher Langley was due to attend the special meeting of Medway Council's health overview and scrutiny committee on Wednesday, but failed to show up.
Instead, new acting chief executive Philip Barnes, who only took up his post in June, was left to face members' questions on his own.
The meeting was arranged after the hospital was rated inadequate by the Care Quality Commission and told it must remain in special measures.
Cllr Vince Maple, who was at the three-hour meeting, said: "The meeting was scheduled on a date to suit Mr Langley. For him not to turn up is rude but for him not to turn up to a meeting on a date that was specifically requested by him is even more rude."
Cllr Maple added: "It was unfair to leave Dr Barnes to speak to the committee on his own. But he answered members questions in a full and frank way.
"He dealt with strong scrutiny from all sides. It was a long and pertinent meeting."
Mr Langley was appointed in February by Monitor, the regulator for foundation trusts, on a one-year contract to turn the troubled trust around.
In June it emerged Mr Langley is paid almost £200,000 a year to work as little as one day a week.
He bills the troubled NHS trust £14,400 a month, plus an extra 10% to cover expenses. His role requires him to work just one or two days a week. If Mr Langley spends one day at Medway, it amounts to pay of £3,300 a day, plus £330 expenses.
Monitor said the pay is in line with other senior positions in the NHS and that the chairman “faces a large and difficult task” at the trust.