Allegiance of the parents most certainly mattered since they were responsible for the child.
What if two anti-American citizens from another country wanted to hatch a master plan to take over the USA.
By the logic used by some posters, these two anti-Americans could:
1. Plan a trip to America and make sure the woman gave birth on US soil.
2. Take said child out of the US and raise said child in an anti-American way.
3. Make sure said child is back in the US by age 21 so he/she can meet the 14 year residency requirement when he/she turns 35.
This person could then be eligible to serve as our President.