Just stumbled across this.
In many states the members of the governing board of a not-for-profit corporation are called "trustees." However, the entity they run is a corporation, not a trust. A not-for profit corporation is nearly identical to a for-profit corporation in operation. However, the non-profit corporation does not have shareholders, and any profits from its operation must be plowed back into the enterprise, or donated for a charitable purpose.
Now, a trust is a different animal. All kinds of assets, tangible or intangible (e.g., a patent, a broadcast license) can be placed in trust. A trust can have a definite length, or it can continue indefinitely. The trustee or trustees owe a duty to a) the individuals for whom the trust was created (as in the case of a trust for minor children, for example) or b) the charitable purposes for which the trust was established (as is the case of some of those foundations who provide funding for NPR programming).
So the simple answer is yes, a trust can own a non-commercial broadcast license. To pass FCC muster, I would suspect that the trust would need to be for an indefinite period of time, and that the trust's purpose would be to operate the non-com station.