Correction: by marking a new message as read (using a browser pointed to the GV page),
the MessageWaiting box will eventually become unchecked, and stuttered dial tone will cease.
This the case even though the message is still present in the inbox.
However, marking the message as unread does not cause the MessageWaiting box to become checked,
nor produce stuttered dial tone.
Not much value in speculating on why this is so. At least stuttered dial tone accurately indicates
that new messages are present.