My husband and I were both in the Army and stationed in Germany when it came time for my son to be born. I was told numerous times that, as a naturalized citizen, he would not be able to run for president. As silly as it seems, this caused my to come home to have my son in the States.
All of that to say that the common information I received as a soldier, in 1977, was that a naturalized citizen could not be president.
In my opinion, they gave you incorrect information. When you are working for the government (i.e. in the military), your children are natural born citizens. John McCain is a natural born citizen since he was born in Panama while his dad was serving in the Navy there.