Scout,Archaeology literally means the knowledge of Ancient (old).In the United States this field is commonly considered to be a subset of anthropology, along with physical anthropology, cultural anthropology, and linguistic anthropology whilst in British and European universities, archaeology is considered as a separate discipline. Thus your statement about Anthropology is totally correct !  (excuse my ... french  ::) )Here a quiz about archaeology:http://bama.ua.edu/~alaarch/trueorfalsegame/index.htm However I believe that Archaeology must be requested whenever no written evidences are found or support discoveries.  Furthermore Archaeology can confirm or contradict written records: It's not because it is written that it is necessarily true, propaganda is as old as the alphabet...

I was led to understand that history began with the written word, which began in about 3000 BC with the Ancient Egyptians.

If you are meaning a written record of history, yes. However, everything that ever happened is history in the wider sense, we just don't know what exactly happened, when, or, to whom. That which happened before writing, then is more properly pre-history, if you will.