The answer is ''not necessarily''. I was born in Australia to British parents in 1952 and therefore am Australian by right. That rule changed in the 1960s to prevent pregnant laydeez using it as an immigration backdoor and travelling to Oz to give birth.
The Aussies were smart enough to do something we've not. There's even a term for them now, "anchor babies", babies born in the US even when at times (often) the parents are here illegally.