Is PicoPSU hazardous?
The rationale behind grounding the cases of mains powered equipment has to do with the fact that one side (the 'neutral') of the AC mains is typically already tied to ground, by the utility company. If a piece of equipment had an un-grounded case, and a physical failure inside the unit caused the other leg of the mains (the 'hot' side) to contact the exposed surface, a potentially lethal hazard would be created; anyone coming into contact with the case and a ground at the same time would be directly across the full mains voltage.

Now consider running from a 12V supply. Some low voltage DC supplies do tie one side of their output to ground, some don't, it depends on the supply. Obviously if one side is grounded, the same possibility exists that an internal failure could energize the case with respect to ground, albeit at only 12V. If you have the output-not-grounded kind, even if the case comes into contact with one of the 12V supply leads, and you touch that case, you aren't likely to come into contact with the other side of the 12V supply, unless you really work at it. 

Personally, I wouldn't worry too much about the lack of an earth-ground in a 12V system. The odds of a multi-point failure that would result in getting one's person across the 12V supply are low, and even if it happens, it's only 12V. But a parting word about 'only 12V' - if your skin is dry, and you apply 12V to it, chances are you won't even feel it, but if you have significant moisture on your skin, especially salty moisture, you definitely can feel it. I wouldn't recommend the experience. Also, even though the voltage is low, you can often get enough current from low voltage supplies to turn rings, metal watch straps, etc. red hot, also un-fun.