juan,

   You are.  Unless it is stated by the documentation for the
class/property/method, I think it is safe to say that lifetime management of
any object passed to the class/property/method is your responsibility.

   Of course, you can always simply assign a stream to the property and
then try to access the stream after the page loads.  If you get an
ObjectDisposedException, and then you will know.  In this case, you will see
that you still have to call Dispose on the Stream implementation when you
are done.