In Australia at least, pretty much any electronic device has to be tested to ensure unintended radiation emission between 9kHz and (I kid you not) 400GHz is within acceptable limits before it gets a C-tick (similar to the CE certification) and be sold.

I think most of the time they stick the device in an anechoic chamber and take measurements at certain distances. For example, under the CISPR 22 standard (that information technology equipment with a supply voltage of less than 600V falls under) it must radiate less than 30dB (uV/m) of electromagnetic radiation between 30 to 230MHz, measured at a distance of 10 metres with a quasi-peak detector, less than 37dB at 230 to 1000MHz, and so on.

There are also restrictions of how much interference is caused from the power supply (which shouldn't apply to the Raspberri Pi) and how much EM is emitted from telecommunications ports on the board (which will apply to Ethernet, but probably not USB).

I am guessing that most PCB/PS -like electronics would pass this without any specific attention, given there were no major manufacturing defects?

I'm a little unsure why TI made efforts to avoid it.. or just because they could?

It depends on how fast things are clocked on your board. For anything less than 100MHz, you wouldn't have to think about it. For faster clocks, you might have to be a little wary (but it should be fairly easy for such a low power device with proper ground and power planes, bypassing etc.)

It doesn't intentionally have any radios, but it's transmitting multiple electromagnetic signals. Heck, when I was in school, one of my EE professors insisted that we'd never see CPU speeds much above 100 MHz because of all the radio frequency noise they'd emit.

As the raspberry pi blog comments say today they actually did find a misconfiguration of the HDMI port that was unintentionally transmitting on all sorts of frequencies. So the earlier than expected certification wasn't pointless.

Power supplies can be tested separately from devices. That is a major driving force behind the fact that almost every device has an external power supply nowadays.

Also, that "it runs on 5v DC and has not PS it should be OK" likely is true, but somebody has to tick some boxes to confirm that the device is safe. And no, that is not a purely bureaucratic thing. For example, there are 5V driven braille displays with piezo actuators that internally produce 200V+ voltages, and could be dangerous. That voltage is present centimeters from the fingers of its users.