It's not something that's theoretical here - I have had multiple hard disk players throw a lot of noise on the headphone output whenever the hard drive did any seeking. It's hard for the battery to cope with those short, high-power drains or so I reckon. While it's also possible the sound if being sent to my earphones by pure vibration, I highly doubt it - it sounds too direct and directly audible to me. It doesn't seem to apply to most other parts inside DAPs, I believe. Or maybe, it's exactly as you say and all those things add noise to the headphone output!
If you have really sensitive IEMs and a hard-disk based player, take a good listen for yourself. It shouldn't be hard to hear at all.
Edit: The screen being on is something you can control (it isn't audiophile with the screen on, imo), you can change the parameters yourself to get proper sound. The hard disk is hard to impossible to control.
In all my years using it, the only time I can hear my iPod's hard drive is either when it's within a foot or two of my ears in a quiet setting, or directly next to my ear; in both cases, that's without wearing any IEMs. I've never heard anything while actually listening to music. Maybe you have golden ears or just bad luck with hard drives, but all I can say is that my experiences have never showed this to be a problem.
Ultimately, my thoughts are as cooperpwc mentioned: I would think the power requirements of a hard drive, screen, etc., would be taken into consideration during the design of a player so as to prevent any such issues as these. Especially for some of these major companies with years and years of design and technical know-how under their belts, it would seem a major oversight to me to do otherwise.