Yes, government is probably too big.
I'm not real surprised that all of the top spots are government, though I think the way the data is presented is somewhat misleading. The government serves many functions whereas businesses tend to be specialized (also, most businesses have competitiors who do pretty much the same thing). If you looked at the number of people employed by industry (government, healthcare, retail, food service, etc) I bet the perspective people got from the stats would be vey different.