Two unrelated events have sparked an uproar in the Island community in the past two weeks, fueled by the power of social media.

Though not a perfect parallel, both were handled in very different ways that speak not only to important questions of transparency and trust, but also to deeper issues around how the Island’s key institutions — and the community in general — respond to changes that necessarily accompany new leadership.

At the Martha’s Vineyard Hospital, trustees swiftly circled the wagons after the abrupt ouster of their president and chief executive officer Joe Woodin on the morning of June 5. Mr. Woodin had been on the job for just thirteen months. Trustees were quick to say there had been no malfeasance, and yet overnight they sent their new CEO packing with only the vaguest justification: Confidence had been lost, there were differing visions, or no, actually it was just a question of management styles. Considering the likely costs of Mr. Woodin’s severance and the time and money it will take to replace him, the reasons feel insufficient.

Meanwhile at the Martha’s Vineyard Regional High School, the strange after-hours painting incident in the hallway of the history department on June 14 followed close on the heels of the departure of Elaine Cawley Weintraub, the longtime department chairman who announced her retirement amid harsh criticism of the new administration at the school. Andrew Vandall, a history teacher who worked alongside Ms. Weintraub, quickly admitted to obliterating the student murals and apologized. Principal Sara Dingledy acted swiftly to address the problem openly, among other things emailing a note to parents of students and gathering her staff to allow a full airing of the incident.

Let’s be clear: it’s hard to attract — and retain — highly competent executives to the Island under the best of circumstances. Martha’s Vineyard is a challenging place to live year-round. There are wild swings in the pace of life from winter to summer. Housing is scarce. The cost of living is in the stratosphere. The sense of community is strong but also fraught with insularity that can turn ugly overnight.

It’s hard to imagine anything uglier than finding oneself in the middle of the kind of controversy Ms. Dingledy faced a year into her tenure as principal of the Island’s only high school, taking over after a long period of instability and turnover at the top. Yet she promptly took ownership of the situation, navigating delicate issues of confidentiality with sensitivity and candor.

By contrast, longtime hospital board chairman Timothy Sweet who led Mr. Woodin’s firing has sought to downplay the crisis and while admitting mistakes, has mostly shied from explanation. Board members are talking to their critics, he said, but these conversations are private.

In the absence of real information, the vacuum naturally has filled with speculation and rumors. Ironically, these are far more corrosive to confidence in Island institutions than plain, hard truth.