> in many environments even hinting that you're looking to leave will... greatly increase the urgency of your search

Just to provide a single anecdote of this, my friend worked as a recruiter at a well known company. If higher ups got proof that you had applied to another job, you would be terminated day of and whisked out of the office by security.

The stories from him and his coworkers of the subterfuge involved in job applications were impressive.