I decided to look it up myself. This is per AR 670-1, paragraph 3-7:

k. Wearing Army uniforms is prohibited in the following situations:
(1) In connection with the furtherance of any political or commercial interests, or when engaged in off-duty civilian employment.

I would consider job hunting "commercial interest" or "engaged in off-duty civilian employment", or at least close enough to make it an extremely bad idea. Since Fox and CNN are always selling slant and refuse to publish unbiased news, I have no idea what really happened, but I'll at least guess that there's another side to this story that we'll probably never hear.