Yes, you could almost see BK's antennae go up. Graham didn't want to be more specific, but it's now out there. Fox isn't following up on it; perhaps they want to let it cook a while yet.
I think the 'antennae' was actually the control booth asking through his earpiece to get Graham to verify. Control booth operator was acting on instinct at first but then thought better or was overridden at which point Kilmeade was just told to get back on topic. There's likely still back room discussion at Fox over whether it's the right time for this. Judge Napolitano already got into trouble there over the same issue remember.