I apologize for posting in the HAI forum but the OP asked and this really sounds more like a general topic.
Dan: I can't point to a specific thread that answers your question or addresses your 'fear', the entire site is full of examples. Home Automation is intended to make your life a little easier and more pleasurable. It can do some of the mundane things for you like simply turn things on and off or it can do all kinds of things based on certain conditions. But as Brian stated, if you build your system with intelligent/standalone subsystems that work completely on their own in the same typical old fashioned manual way and use a central controller like the Omni, if anything happens to the main controller or even any of the subsystems, you should still retain a basic level of functionality. Sure you may lose all the automated controls and logic but you should still be able to operate your lights, HVAC, garage door, irrigation, etc. Alot just depends on how you do things. Just as a few examples - you mentioned garage door, well that is simply putting a contact closure across your existing button, so the controller can trigger your door to open and close or you just do it manually with the button same as now. If you had something like (not recommended, just an example) your garage door automatically opens when a motion detector is tripped, if the main controller is down that would not work, but your old buttons still do as normal.
Now like I said it depends on how you do things. On the other side, I personally have my irrigation controlled via relays on my controller. If my controller fails, yes, the way I have it setup I would lose ability to turn on irrigation. But I chose to do it that way as I consider irrigation non critical and I could live without it for the few days it would take to repair/replace the controller. But - there ARE othe ways to do it where it can be controlled by the controller OR manual.
So, I would not really worry about a safety concern or anything by introducing automation. Could you open your garage door and disarm the security system when somebody opens your mailbox? Sure and that would be really bad and unsafe, but that is a purposeful set of programming you would simply not do. HA is great and safe if designed and setup properly.
Hope that helps a little - if not, please post more specific questions.