That's indeed the key idea behind determining an MHT root.

Let's consider any possible longest path LP between any two nodes.

There would be a unique middle node M for odd longest path lengths and two middle nodes M1,M2 otherwise.

Now, if we consider a leaf L on LP , it's easy to see that

distance(L,M) = max (distance (L1,M)) for any leaf L1 on some other path (non-longest path)