It's hardly an unexpected direction, considering there's a NOTAM
instructing you to do exactly that:

In an emergency, one can disregard NOTAMs. And if there are clouds,
you'd be dodging clouds as you try to make your exit. The flight would
look erratic and would attract the attention of big fast airplanes with
guns and missles.

I would consider a communications failure in the ADIZ to be a DIRE
EMERGENCY and would take what steps I thought prudent to stay alive. If
there's an airport below me, I'm probably not going to futz with trying
to thread my way among some cloud for twenty minutes to exit the ADIZ
just because of a NOTAM. It would not be prudent to assume that the
fighters that are scrambled won't pick me to make an example of that day.

Outside the ADIZ, a non-event. But the ADIZ can become a war zone in an
instant. It's a stupid construct, it has to go (along with the FRZ),
but until it does, aviators are depending on everything going right.

We've been lucky so far. But just lucky.

Jose
--
You can choose whom to befriend, but you cannot choose whom to love.
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