There are a couple mistakes she makes. First off, she cites cases that are the result of importation of measles, rather than sustained endemic transmission, and claims that measles was never eliminated. She apparently does not understand that "eliminated" means the sustained, endemic transmission no longer occurs. Second, she scoffs at the 1-3 per 1,000 risk of death from measles because there has not been a measles death since 2003. But is she right to do so?
Let's start by counting up all of the cases that have occurred since 2000. We get 1,372 cases. If we look only at cases since 2003, as she does later on, we have 1,126 cases. She makes the assumption that there was one death in 2003. If that were true (it's not, more on this in a second), we find that the death rate was either 0.7 per 1,000 or 0.9 per 1,000. Close to the 1-3 deaths per 1,000 cases figure. But, there were actually two deaths in 2003., according to Epidemiology of Measles - United States, 2001-2003. So the rate is actually 1.6-1.7 per 1,000, depending on whether you start with 2000 or 2003. That's comfortably within the expected rate of death from measles.
[Edited to Add (2/24/15): According to the Summary of Notifiable Diseases - United States, 2012, there were several additional deaths from measles during the 2004-2010 period. There was one death in 2005, two deaths in 2009, and two deaths in 2010. A search of the CDC WONDER database, which stores national vital statistics information like cause of death, uncovers additional measles-related deaths. Some are acute deaths caused by measles, measles encephalitis or measles pneumonia, for a total of 10 deaths during the 2000-2012 period. But there were also 32 deaths from subacute sclerosing panencephalitis (a relatively rare complication of measles that occurs after a patient seemingly recovers from the disease without any other problems; SSPE can manifest anywhere from weeks to years after primary measles infection, causing a slow, agonizing death) during that same period. With a total of 10 acute measles deaths during that period, we have a rather high mortality rate from measles (~7 per thousand cases). If we include the total number of measles cases for 2014 (644 cases), we've had 1,887 cases of measles since 2000. That puts the death rate at around 5 deaths per 1,000 cases. Still high, but closer to what we would expect to see given the number of cases. At this point, I don't have any information on why it is so high, but it could be due to underreporting of measles cases, measles being misdiagnosed as another illness, mild of asymptomatic cases of measles, etc. Without additional information about these patients, we can't really say much more about the why or how of these deaths.]
That's a very simplified way to look at the numbers. We would expect to see anywhere from 1-2 deaths per 1,000 cases to 1 death per 3,000 cases. And when we look back at recent measles outbreaks in the U.S., we see a figure that fits that estimate. The problem is that we don't know who will be that 1, nor out of which bunch of 1,000-3,000 cases. Every single person who gets measles has that risk. We might see a dozen deaths in some outbreak as a statistical fluke, where each of those 12 happened to be the 1 in a 1,000.
This is where the anti-vaccine activist will try to continue to ignore the impact of measles by looking for any flaw in the decedent's health. If they were not 100% perfectly healthy, then clearly it was whatever illness they had that did them in. It's a very callous way of looking at things and shows a gross disregard for others. This is not surprising, as anti-vaccine types tend to be very centered on themselves, taking a "me and mine (but mostly me)" stance, blissfully ignoring that they cannot know if they or their children will be that 1 in 1,000. To even consider that would threaten their worldview, so cognitive dissonance sets in, and they sail blissfully on.
With the recent increases in measles cases (as of today, May 9, there have been 161 cases already this year, an alarmingly high incidence), it is only a matter of time before we not only begin to see endemic transmission, but more deaths. But that doesn't have to happen. If people vaccinate, we can bring the incidence back down. If enough people are immunized worldwide, we can eventually completely eradicate measles. If we can do that, then we won't need the
Time and time again, anti-vaccine folk display an astonishing innumeracy. Whether it be trying to argue the disease isn't dangerous and proving themselves wrong with their own numbers, or not understanding what happens in an outbreak when we're dealing with large numbers, anti-vaxers and math just don't mix.