Mr Kennedy, the local MP, spoke out after his was among more than 100 applications for the Applecross Trust in Wester Ross to be rejected by the six landowners who run it. They had requested to be members of the body, which owns the 61,000 acre Applecross Estate, but enjoys charitable status.
In September, campaign group Land Action Scotland, led by land reform advocate Andy Wightman, announced that 90 applications had been lodged seeking membership of both the Applecross Trust and Mount Stuart Trust, which owns 28,000 acres on the Isle of Bute, to make them locally accountable.
In a letter to the trust, Mr Kennedy, the MP for Ross, Skye and Lochaber, said: "Many of those applying, including myself, have only the best interests of Applecross and its people in mind, and a greater connection to the peninsula than many of the trustees. I believe that the interests of local communities are best served by locals having a say in the management and running of their area."
Caithness, Sutherland and Ross MSP Rob Gibson said: "This smacks of the worst kind of 19th century landlord arrogance and is something that should be consigned to the dustbin of history. Their assertion that they speak for the community is questionable."
The charitable trust has no shareholders, only members who are directors and there are no restrictions on who can join. It is chaired by Richard Wills of Andover in Hampshire, whose family, the Wills tobacco barons, bought Applecross in 1924.
An open letter was issued by seven Applecross residents, saying that 110 had signed a statement of support for the trust, a majority of the 200 population, but this has been challenged locally. However, landowners organisation Scottish Land & Estates said the local people had made clear they didn't want Land Action Scotland.
Archie MacLellan, the trust's administrators, said: "Recently, we have witnessed the Land Action Scotland campaign which ostensibly wanted to improve local accountability. In reality, it is a politically motivated campaign to gain control of the Applecross Trust."
Alison Macleod, secretary of the Applecross Community Council, said: "There are local applicants for membership of the Applecross Trust, I am one and I know of at least three others. My husband Alasdair asked three of the trustees in March, why there was no local representation on the trust and was told that a local person could not make dispassionate decisions as a trustee as he would be too emotionally attached to the place.
"She said the trustees had been reluctant to communicate with the community. We have had one formal meeting with trustees this year. Nine weeks after that meeting we have had no response from the trust to the points we raised."