It was weird how I personally responded to that statement. I have lived overseas since 2005. First I was stationed at Osan AB, Korea and then RAF Mildenhall but for me, I did not become an expat until I was on my own in strange country. After serving my country for 10 years, I had no support from the US government not even during my time while I was unemployed but I am crafty and planned ahead so I had enough to carry myself until I did find work. Also I had the amazing support from my husband!
The reason why I do not consider military and US Embassy personnel and their dependents not to be expats is because they do not really live in the country on their own not the way expats do. If you have to live on the economy with only the same resources as the locals have, then I consider that person an expat. That includes people that move overseas with their companies. Most of the time they have little support in living in the other country and most certainily are not exempt from paying the same taxes, fees and prices that locals have to.
This doesn't belittle the experience of those stationed overseas at all but I personally don't think that being stationed overseas considers one to be an expat. You are very fortunate to live outside of the US and experience life overseas but it is very different to what the expats are experiencing. But I think that the real thing is, I have been on both sides so I know what it is like living both ways.
Nonetheless enjoy it!