That's the weird thing about it. I'm pretty sure that my old Toshiba laptop with LED-backlight and my current Lenovo work laptop with LED flicker visibly more than, for example, the ipad 2. Yet I do not get a headache out of them. Also, my new 27" screen, also LED, doesn't give me any problems what-so-ever, which makes a long time sufferer like me very happy - believe me.
However I couldn't stand looking at an eee pc (again, appeared to flicker less) or one BenQ full hd monitor. So you're right. It has very little to do with flicker in general and everything to do with the frequency, or possibly some oscillation(?) if the flicker is not completely even. Even between manufacturers there can be big differences. As for the iPhone, I don't own one. I've never had any problems when I've used one of my friends' but lacking long time "exposure" I can't be sure.
The problems appear to get worse the darker the screen (or lower rate of flicker) and better if the screen is at full brighness. Also, futurewise around the corner, OLED screens may be better since each pixel is lit-up separately with a different flicker rate should the brightness be different, and thus cancelling each other out and making for a near non-flicker picture. But I'm just guessing here, no real experience. And yup, I'd wish I could use the iPad as much as I wanted to, and owning an android phone (2.3) with a big screen I know that androids are not quite there yet software, quality or usability-wise.