I'd suspect it differs from person to person. I guess I answered as I did because the way the question was phrased set up what seems to me to be a false dichotomy.
When you say "perk", I think of something that's offered to attract employees because it goes beyond what's typically expected from a baseline office (be it free soda, gym memberships, or $3000 chairs).
When you say "necessity," I think of something the employee can't be reasonably productive or present without (a desk, an internet connection, a keyboard, a restroom).
There's a lot of stuff that fits in between or outside those two categories. There are things that are above the absolute necessity baseline but too much within the level of expectation to be considered a perk. Free coffee comes to mind. So does a microwave in the break room/kitchen. Or (on the west coast) a casual dress code.
Others aren't there specifically to make the job more attractive to employees - but may have that effect on some (an open floor plan; a well defined professional development ladder). You'll notice that some of these are neutral or a turn-off to other employees. They also tend to be things that the company leadership will help make the company more effective.
So I don't see something like allowing headphones while working as either. It's too mundane and expected to be a perk; and as an employee I may consider it a necessity, but I'm pretty sure my employer just sees it as part of a relaxed culture and a way to mitigate the distractions of the open floor plan.
Naps are certainly not a necessity from almost any employer's POV. An employee is generally expected to be able to be productive without one; and they're far from an expectation in any job in the US. They're certainly not necessities. For some employees they'd be seen as a perk, while (as this HN discussion seems to demonstrate) others would disdain a culture that accepted naps. But I suspect that companies that allow them consider them to be a part of the culture rather than a perk - something that's less about making the job seem attractive and more about creating a more pleasant and effective work environment.
Does that make any sense?