Numerous PDF scripts for non-official POW/MIA ceremonies reference the bible, but it seems it was thrown in more as an afterthought than an actual part of the ceremony. The only official doc I found had no mention of a bible. https://www.62aw.af.mil/shared/media/document/AFD-120524-091.pdf
The most annoying thing about the Fox News article, though, was that they incorrectly argue that the first amendment's freedom of speech allows those that are pro-religion to force official military events to continue with religious nuances or have religious undertones. I don't know about you, but I always feel a little bit weird when at a commander's call or an awards ceremony or any other random event, the commander or chaplain starts praying, sometimes even prefacing it with something like, "If you like, join us."
I can always look up and see that, while there are plenty of guys going along with it, plenty of truly Christian people in the Air Force, there are also a good 1/4 to 1/3 of the people there wondering "WTF is going on?"
Forcing religion directly into the mainstream military culture is not something that the AF should be doing or caring about whatsoever. The point of religion is to help bolster someones personal spiritual life.