...

What I expect when I see an immutable field is that,
literally, the value of the field doesn't change over
time, no matter what happens.  Thus I can cache the
value in the client side, for example.   Or I can avoid
locking to read the immutable fields, for no other thread
can possibly change their values.  It doesn't matter
whether the value can be changed by "private" methods
or not.  What matters is whether the value will ever
change or not.