i work and am currently in school still in the radiology field, so i have a little bit of knowledge in the area of radiation.
As far as i know ((i will state why in a second)).. i have never taken a Geiger Mueller counter to the devices i use every day.. cell phones and laptops do not emit ionizing radiation (on a large scale, there is some emitted and that amount is regulated by the FCC, and i have seen mass publication articles about which cell phones emit the highest radiation level,, while still being under the regulated levels).
They and other electronic devices do emit waves on the Electromagnetic spectrum; radios, tv's, .. its endless.. we are a wash in a sea of RF, wifi, and various EM waves. All of which travel at the speed of light in a vacuum and have characteristic wavelengths, frequencies, and energies.
Energy is the key measurement, they must have a certain energy to interact with various types of matter, and the matter in question is the kind around your lap. The ones that you are asking about -i believe- is the kind of EM radiation you imagine when thinking about Chernobyl and 3 Mile Island. These are probably not emitted by our iDevices because of the simple fact that they do not have anything radioactive in them. They do not have any radio-nuclides that emit alpha, beta, or gamma rays; and they do not bombard dense metals with high energy elections to create x-rays, this is whats done when you have hand broken and an X-ray is required).
What our iDevices do have is thermal radiation (THIS IS NOT on the Electromagnetic Wave Spectrum) and some Electromagnetic waves from the EM Spectrum. The EM radiation that cell phones and TVs use are very specific to their devices, just like the AM/FM radio in your car. They operate in the microwave range, they do not have the requisite energy to interact, ionize, with human tissue.
What your concern should be is HEAT, and thats all that was described in the thread you linked. Thermal radiation is different than ionizing radiation (x-rays, gamma rays). Thermal radiation is the jostling of molecules and atoms, increased movement means increased friction and increased heat from the friction. Just think about the water boiling on your stove. What the x-rays and gamma rays (and UV rays in few very specific instances) do is remove electrons and change the electrical charges of the atoms they interact with (this is called ionization).
I believe the concern of heat (thermal radiation) from laptops is very real, but the concern of ionizing radiation is almost nill, because there isn't anymore in the iDevices than what we are not getting everyday from the natural sources of ionizing radiation. What does merit research is wether or not the increase amount of microwaves and radio waves can change our biology.
hope that helped, hope i didn't upset anyone.