So recently I decided to research the truth of this, and found this paper: Body Weight and Mortality Among Women. I recommend reading it if you can access it; I don't think I should make it public since that's probably illegal, but I will summarize as best I can.
The researchers took questionnaire data from more than 100,000 American female nurses of 30-55 years, about all sorts of things like weight, height, physical activity, smoking and other risk factors, medical history, waist/hip measurements, etc. They also followed up the initial survey every two years, and tracked how many nurses died during the 16 years of follow-up (by searching state/national records for causes of deaths and stuff). So it's pretty thorough.
So here's what they found:
When considering all the women that died during the study (4,726), they found that the body-mass index (BMI) in which the fewest women had died, relatively, was considered normal weight, 19-26.9. So these had the lowest mortality risk. Those with the highest risk were the heaviest women, of BMI 32 or more, and those with BMI below 19 had about 25% more risk than those of "normal" weight.
However, when they only considered women who had never smoked (1,499), they found that those with BMIs below 22 had the lowest risk, and it did not increase as BMI decreased. So there was no "underweight."
Then to try and eliminate bias from weight loss due to sickness, they only considered women who had died at least four years after the beginning of the study, so not the women who were underweight because they were going to die soon. They found then that those with the lowest risk had BMIs below 19!
This result was even more clear when they only considered those women (531) whose weight had remained stable (less than 8.8 lbs variation) over the past four years.
They found that the heavier people were, the more risk there was for death from cardiovascular disease, cancer, and other causes; so basically more risk for all major causes of death the heavier one is.
Some limits on the findings: they estimated that 98% of the participants were white, so the results might not be as applicable to other races :/ I dunno. Also, the more people they eliminate in order to control for variables, the less reliable the results are; so there's more risk of error in saying that stable weight is good than in saying that low BMI is no worse than normal BMI.
If anything's unclear or if anyone has any questions, feel free to ask!
So in case anyone was worried about being unhealthy by being underweight, here's some hope :) Next I plan to look into the idea that being underweight means more risk for osteoporosis, and see if that's true for naturally thin people.