Don't know if someone else already brought it up, but this question is closely related to this one:
If you find someone who just slit his wrists and he tells you 'please just let me die', would you call an ambulance?
Now you can argue that this is not the same situation as with a JW who has his signed medical directive while (supposedly) completely sane.
And it isn't the same situation. The suicidal person states his wishes while dying, he makes an active choice when it really counts.
A JW medical directive however was signed while using armchair philosophy.
The JW doesn't really know what his decision would be at when he was really dying. If he were conscious, he might have changed his mind now he's really in the situation.
For those coming up with alternative examples, e.g. suppose you found someone whois not depressed but slit his wrists anyway, and tells you 'please just let me die. I am dying of a terrible painful disease anyway, and my whole family was just murdered'. Would you call an ambulance?
Now it's more likely you just let him die, right?
And what if you know that what he believes (terminally I'll, family murdered) is actually not true at all?
In the examples above, does the wish of the person trump he need to help him?