You are if the paperwork gets approved after your marriage and you get permanent legal residency (as a result i.e., the vaunted green card). It's often easier for the alien to go back to her country after the marriage because it can take as little as six months to apply for and get a permanent residency visa. When you stay here after the marriage, it's a slightly tougher row to hoe because you have to convince USCIS that you didn't enter the country with the intent of getting married, that the marriage is legitimate, etc. (You always have to prove the marriage is legitimate, however.)
My wife and I have been through this nightmare - although she's a citizen now - from start to finish (we were married overseas 10 years ago).
It looks to me as if this woman had indeed been duped by the notario.
The easiest way to do this is a fiancee visa, which takes the least time to process. While that's being processed the U.S. citizen can hang out with the fiancee overseas, but he/she has to wait for the visa approval to come here. Once granted they come to the U.S. and are married within 30 days.
Foreign spouse gets immediate "conditional" permanent residency, but the "legitimacy" of the marriage must be verified with documentation and interviews after 2 years. The "conditional" part is then removed, the spouse is now a permanent resident in perpetuity but can apply for citizenship after year 3 (not 5 as for other immigrants).
It's usually another year for the citizenship interview/testing, so 4 years total for a spouse.
Still, my experience was that it was a bothersome nightmare and I was very happy when we were done with it.