The place I used to work at only a few years ago rarely had an updated careers page, it took an act of congress to get something added/removed it was almost always wrong (jobs that didn't exist, that were filled, and openings that weren't listed)
Just looked and my current employer has an opening on the careers page that I know for a fact we're not hiring for at the moment.
Just looked and my current employer has an opening on the careers page that I know for a fact we're not hiring for at the moment.