I also agree. I took, and encouraged my classmates to take, several PRN jobs. When I was offered a first full hospital acute care position, I was told that the work I'd done _COULD_ disqualify me from an internship/residency, but that they would work it out with HR to disregard the few months I'd put in before that application was reviewed. Even though I turned that position down, it demonstrated that things aren't as rigid as the OP's advisers suggest. Another classmate worked all year in LTC and now has the job of her dreams lined up -- every path is different.
If you have the luxury of not working, that's an entirely different thing, but after a while, yes -- it will affect you. If you've been job hunting for the preferred position, I hope you've been working on your BSN concurrently, because that's the only excuse for stalling to go to work, in my opinion/what I see as the opinion of employers. I could be wrong. I went from ADN straight into BSN program because I didn't plan to work immediately. But, I then decided to earn some cash, took the PRN jobs, then it seemed like jobs offers started coming in kinda fast.
Do not overlook your classmates/peers -- they're all out in the job force now, right? Lean on them!! Every job I've gotten has been because a peer let me know it was out there or put in my name or handed off my resume and do I ever appreciate it! I think the offers also came because I demonstrated I'm willing to work/willing to drive and those facilities have legitimate shortages.
I do know people who, when they apply to positions are very set on only working a certain job, during a certain work shift, in a certain location. People with those sorts of limitations don't seem to be getting job offers.