I feel sure I cannot be reading the rules right, as it seems to imply that Daemonic Psykers can suffer Perils.  While this does balance them, it also makes almost no sense in terms of the fluff.  So, have I read wrong, or are Daemons also subject to the warp's capricious whims?  

If I remember correctly daemons can cause the phenomena and perils of the warp, but are immune to it themselves. At least this is the case of dark heresy daemonhosts. 

 They can cause both psychic phenomena and perils, and they're immune to the effects of phenomena and not perils. And, without arguing fluff, there's one very good reason for this: Daemon Dust. While rare and hard to get, this is a drug that lets you get the Daemonic trait.

Nice if you're a combat guy. A gift from the gods if you're a psyker. Now, imagine if it made you entirely immune to perils. Would you want that psy rating X psyker popping that and then gleefully pushing every single power he throws, completely safely for the duration of that drug?

 plus demons are not one bit happy family, sure your a demon generally your pretty safe when useing psychic powers after all your drawing on the power of your own plane of existence, but sometimes you do mess up and leave yourself opened, weakened and your enemies or just oportunistic demons will take advantage of that.

plus the chance to have trouble with there powers is one of the costs demons pay to exist in the material universe, there physical forms are flawed compared to there spritual ones in the warp.

In the wargame, only a few daemons of Tzeentch are protected from perils. So… yes, even daemonic psykers have problems when they meddle with the warp because it may sever their anchors that hold them in the Materium.