Make either the Person constructor "internal", or make the _people list accessible by an internal property, so the Person constructor can add this to _people right after creation.
Of course, this solution is not perfect since it will still allow other classes belonging to the same domain assembly wrong usage of your objects, but at least it will forbid any wrong usage from outside (which is typically sufficient for most real world cases).
If you are thinking of a more restricted model, where only the Person class can access a certain method of Organization, or vice versa: the C# designers did not implement such a thing, AFAIK intentionally. See, for example, this SO post and the topmost answerSO post and the topmost answer.