No. If you hadn't added "she thinks" to your sentence you would be correct - but the if condition is false (the risk is worse than 1/40) and so she should get the vaccine.

Where are you getting the measles risk from?

All the numbers I can find put the risk of measles in the US at a couple of orders of magnitude lower than 1/40. About 1000 cases a year in a bad year, 320 million population, 80 year lifespan give about a 1/4000 chance of getting measles sometime over your lifespan.

This is complex. Measles risk depends on how many other people are vaccinated. Right now the US is above herd immunity rates meaning that for everybody the risk is insignificant. However we are close to a tipping point, if vaccination rates go much lower the risk for everybody increases dramatically (but how much I don't know). Note that risk for everybody is just that: for some vaccinated people the vaccination doesn't work (As I recall it is about 95% works) - the risk is drastically higher for the non-vaccinated of course.

If it is only one person in isolation asking this question the risk of vaccines is worse than the risk of the disease - but if more than one person asks this questions the risk of measles for everybody is higher.

There is also the risk that some mutation of the virus will evade the current vaccine. I don't know how big that risk is (the flu mutates such that a new vaccine is needed yearly), at which point everybody is vulnerable. If enough people are vaccinated the disease has many less opportunities for this and will die.