I'm surprised to learn that the copyright of a letter belongs to the sender (or his estate) rather than the recipient.
The statement also mentions that letters from "other family members" (i.e. not JRRT) to Hilary Tolkien are protected by the Tolkien Estate. That makes it sound as if they have very wide-reaching control over the output of the whole family! I do find it suprising that they feel such an acute need for "privacy", so long after the deaths of JRR Tolkien and his brother.
Except from the fact that the other family members might all be still alive! And so might be that these are the persons who run the Tolkien Estate... so when you want to publish any of their letters, you should at least ask them if this is possible.