Interesting, (and a bit terrifying) concept and very Western.
I think it would be more accurate to say we are born without sanctifying grace - a position we inherit from Adam. By being born without this grace, we cannot follow God's Will or merit eternal life. St. Aquinas makes the distinction more clearly than most. It is an absence of grace, rather than an actual "stain" that we are born with. We are not born into evil, but we are not born with the capability to choose God's Will freely. There is a difference - which better explains Catholic doctrine that says that we are wounded, not evil, by nature. Of course, if we were evil by nature, then how could Christ take on our nature?
Regards
The Bible says that you are born DEAD and born IN Sin. All Sin is evil.
Do the math.