The confusing thing is, this isn't really the sort of test that comes back positive or negative. It just adjusts your odds. For example, everyone has some risk of having a baby with Downs syndrome. If you are 35, this risk is about 1 in 200. They then do this blood test, and based on statistics, they can adjust this risk to be higher or lower. If the adjusted risk is worse than 1 in 200, they call the test positive. If it's better, they call it negative. So you are still going to see people with 'negative' tests have a baby with Downs. You are still going to see a lot, most, in fact, people with positive tests have baby's without the disease.
The reason the test is called 'positive' at 1 in 200 risk, is that this is the same risk of losing a baby with an amnio. So a positive test basically means that your baby has more of a risk having the disease (whatever it tested positive for, I just used Downs as it's most common), than you are risking losing the baby with definitive testing. Your age is really important too. If you are 45, the test may actually lower your risk of a baby with Downs, but it still may be large enough to be positive.
So the more important information for your friend is what her adjusted risk turned out to be.
The level of these hormones depends on the size of the baby. So being off in the dates is a really common reason they are wrong. An amnio is also the only test that will give you a real 'positive' or 'negative' answer. (not perfect, but pretty close). Even a level II U/S will only adjust your risk.
The only other factor I can think of to mention is that you didn't say what the test was positive for. I'm guessing a genetic problem, since she is being sent to a genetics doctor. And all the above information can be true for Trisomy 13 and 18. You actually get an oppostite result (low vs high hormone levels) on the AFP for Downs vs Spina Bifida. Spina Bifida is much easier to look for on ultrasound than Downs.