Any group that would eventually pool their resourses together would technically form a "government". True?
Absolutely true. (+1) You just need to distinguish between the legitimate form of government (voluntary) from the criminal form of government (State).
Unless you're a hermit, anarchy requires voluntary government. People intuitively understand the need for government. Because they have been falsely taught to believe that anarchy is devoid of organization, or government, leading to chaos, it's probably better to use the word anarchy only among radical libertarians and, instead use the term voluntary government, or private government when communicating with the uninitiated.