May have found an answer to my own question.
Fox News anchors, during the "Fox & Friends" morning talk show
that produced today's on-air snafu,
were prepared to ask,
What does Ann Kirkpatrick have to say about
being in support of ICE?
(In fact they did ask. You noticed what happened.)

Here is what Newsweek reports.
On July 19 (this past Friday), a forum was held
by a super-PAC named "Represent Me Arizona"
in which Marian Chubon -- spelling? -- is active.

The forum of election candidates included Ann Kirkpatrick.
Before the live audience (Congressional District 2),
the forum moderator asked for a show of hands from the candidates
of those who would
"support ICE agents without any increased oversight."

And the booing began, because Kirkpatrick silently raised her hand.
Newsweek says that it reviewed a "heavily edited video"
released afterwards by the super-PAC.
The video showed no direct statements about ICE, pro or con,
coming verbally from Ann Kirkpatrick.

Unless FOX News had access to something else that
I have yet to turn up in my searches,
it was based on the publicity around this super-PAC forum
that Ann Kirkpatrick is publicly viewed as
supportive of the ICE.
That this recent event
is the reason that FOX News went through the motions (?)
of booking an on-air contact with "Ann Kirkpatrick."

Well, this has all happened within the last twenty-four hours
(the on-air snafu, I mean)
so it will interest me to see
how Kirkpatrick responds in the very near future.

We'll see if she makes a different impression
from the person who surprised FOX News this morning.

As for Kirkpatrick's campaign,
the state primary election date is late August --
roughly four weeks away.