In the case you cited, the father, while a naturalized US citizen and an active duty service member at the time of Thomas’s birth, his father did not meet the physical presence requirement of the statute in force at the time of Thomas’s birth. If his father had met the physical present requirement or had been born a US citizen, the ruling would have been different.
The best outcome that Thomas could have had, if his father met the physical present requirement or had been born a US citizen, would be becoming a naturalized citizen by operation of an act of Congress. Thomas was arguing to get out from that "Act of Congress" means to citizenship. His argument was that he was born in the US, because US military bases is no different of that of one who was born on US 'soil'. The court rejected his argument.
Your statement, "birth [on a US military base abroad] and 'natural born' citizenship is no different of that of one who was born on US 'soil'." is false.