Yes. There have been presidential candidates who were born on US territory, but outside the United States proper, and there was no real controversy about it. John McCain was born on a US military base in Panama while his father was stationed there. Barry Goldwater was born in Arizona Territory before Arizona became a state. Both were considered natural born citizens even though they weren't born in what we usually think of as the United States.
In fact, US law is fuzzier on this issue than most Americans realize. Most Americans born in a foreign country to an American parent who returned to live in the US are also considered “natural born”. (Ted Cruz falls into this category.) Because the Constitution uses the phrase “natural born”, but doesn't define what that means, plenty of case law has built up over the years to include these Americans among the natural born. It is not considered a controversial issue in constitutional law.
More specifically to Gabbard, her mother was a natural born US citizen and her father was an American Samoan who became a naturalized citizen. Gabbard moved to Hawaii at the age of two. American Samoans do not automatically have natural born citizenship (like Puerto Ricans do) but are considered US nationals. If she had been born to two US nationals in American Samoa, then she wouldn't be a natural born citizen.
***Answer not my own. Found online
