This is why I used those two examples - the murder did act, but if he acted with a certain "idea" in his head he is guilty of one crime, if he acted without that idea it is a different one. If the mushroom guy picked those mushrooms in ignorance, he is not guilty, if he picked it with a particular knowlege he is not - both involve action but the crime depends upon his mentality.
Don't get me wrong, I am uncomfortable with the notion of thought crimes and of course the concept is overly broad, as you say, thought alone is not yet a crime, I am not sure if intent alone is a crime but suppose I have a couple of chemicals that can be gotten anywhere and I have a file on my computer on how to make meth, I could be convicted for intent to manufacture - there is no way for them to determine intent except for that file, and so that is the only proof they have that I may have had such intent, the chemicals could be for a variety of uses.