You (both) miss the issue/concern. Some threats are merely that, threats. Some are more like warnings/promises.
While all threats are a matter for concern, most people are all bluff and posture. But once a threat is carried out, the next threat must be treated differently.
I don't condone the network execs' actions... but I understand them. It's not because the threat is an Islamic threat per se... it is because the fanatics professing to represent Islam have shown they will act on their threats.
That changes everything if you have responsibilities to others, (let alone your own personal love of life.) I would be just as outraged if I was put at risk working the front counter while that executive sat safely on the top floor.
That said, those who accept compensation for "protecting" us have a duty now to pursue the perpetrators of this threat to the full extent the law allows, lest it embolden the threateners and those who watch them... just as we did following the oklahoma city bombing (a non-islamic action.)
The follow-on threats were treated with the same level of concern as in this case, imo.