I will tell you how it sounds to my native ear.
When I hear, "He couldn �t board the plane," I think, "Did he not have his passport or driver �s license?" In that case, he would not be allowed. But there could have also been a mechanical problem with the aircraft, something blocking the entry, or maybe he was struck by fear, or else he fell in the hall and broke his leg. There are other reasons besides permission that someone "could not" do something. Permission is implied but these same words may be used other ways.
When I hear, "He could board the plane," I think of his choice. If there is no one denying permission then "could" leaves it wide open to the actor to make a decision. Then the sentence might lead to what other choices exist. You could still say, "He could see the patient," to indicate permission; I, for one, give you permission. But the word in the affirmative is more likely to express choice.
"The visiting hours were from 5 to 6 so he could see the patient after work."
"He had lost his passport, but since he had a driver �s license he could board the plane."
These sentences are fine.