The only way to answer this question would be to conduct a study, control for other variables, and determine (with statistical significance) that birth order–and not choice of degree, intelligence, opportunity, finances, ages of the parents, health of the parents, individual personalities, etc–is The Reason people decide to move away or stay close to home. Would such a study even be possible, due to the amount of confounding variables?
Anyway, since this is IMHO–your hypothesis doesn’t hold true for my family. My younger sister and I both attended college roughly equidistant from our hometown. She moved further away for her first job (Indiana to Wisconsin) and then waaay further away (Wisconsin to Texas) for her 2nd job. I was still living close to my mom when my sister moved to Texas. Within a couple years of that, though, I moved waaay far away for work (Illinois to New York).
So my younger sister and I were both equally willing to move far from home, in the end. I’d have liked to get away sooner, but I couldn’t afford a cross-country move prior to that.