Typically speaking HR doesn't just look on Linked, CareerBuilder, etc to see if your resume is up there or even recently updated. Even if they did see it that on it's own is a non-issue. (Many of us keep our resumes up to date and recruiters at arms length just in case)
There is a catch though. Not all jobs tell you what company they are for upfront, sometimes they wait until you have your resume passed on by a recruiter. As you can imagine applying at your own company unknowingly goes badly. In addition there's always the "people know people" issue. When your resume lands on someone's desk and they see a company they know someone at they might ask. When your boss gets a call from his buddy asking if you're any good... yeah... it'll be embarrassing at best. (that actually happened to me, I managed to turn it into a raise but for a while I figured I was getting a permanent vacation)
There is also times where an employer thinks you might be looking and digs around to see if they can confirm it. Usually this gets pretty shady and most companies wisely avoid such behavior as it can lead to litigation.
In the real world if your employer makes a stink about you having your resume online they are being unreasonable. If you mark yourself as "actively looking" though that's on your mistake.
Most of the time you can pursue job opportunities discretely through recruiters with little to no worry of it coming back to haunt you. There are exceptions, but so far I've only had my current employer find out once which I was able to down play and turn into a raise. (which the lack there of was what triggered the search)
If you strongly suspect your company of such behavior that's a major red flag of serious company health issues and you're probably right to seek a new employer.