Nice plant.
I don't think you can generalize (or universalize) like that about a diverse genus with thousands of species. Euphorbia roots can be really robust. Some Euphorbias react really poorly to winter water. Many Euphorbias do not burn under full sun (there's plenty of them here that get nearly day-long sun with no ill consequences).
The plant in the original post looks good to me. Be careful not to put it in too big a pot. Maybe 4" to start with, wider than deep, with fast draining soil. It may lose some or all its leaves from the stress of being bare rooted and moved to a new home, but that should be entirely reversible once it gets started again. Find a place with lots of light if the plant will be indoors (try to max out the light and place the plant close to a very sunny window) but if it will be outdoors, it will require protection from overhead sun (bright shade or filtered light would be best outdoors, at least for starters).
Wait a week after potting up the plant to water deeply for the first time.
