That’s not what Roe stands for, hence, that’s why abortion has been regulated since Roe. (parental notification, 24 hr waiting period, etc.).
“most laws against abortion in the United States violated a constitutional right to privacy under the Due Process Clause of the Fourteenth Amendment.” Notice, most, not all.
Most importantly, there is a late term exclusion inherent in its holding. “The central holding of Roe v. Wade was that abortions are permissible for any reason a woman chooses, up until the “point at which the fetus becomes ‘viable,’ that is, potentially able to live outside the mother’s uterus, albeit with artificial aid.”
http://en.wikipedia.org/wiki/Roe_v_wade
Your main point though, “Americans don’t have a clue what Roe v. Wade means” was proven right by your post, no offense.
Read the case. Parental notification was considered to be such a pitifully minor “regulation” that it did not count. But any significant regulation of the “right” of abortion is prohibited. And I would also point out that the courts have even been very prolific in striking down even parental notification laws.