I think the use of the word “ideal”, particularly being that it’s in quotes, is telling. As others said, I imagine it’s more of a choice by the doctor to attempt to make a realistic goal that is not terribly unhealthy but also not discouraging. Either way, if and when she meets it, the doctor can always reevaluate, or she can make further decisions herself.
Another thing to consider is that there very well may be some truth to what she says, even if it’s a bit skewed and I’ll use myself as an example. I’m in great shape at 6’ 230 (which is obese by BMI standards) and yet my ideal weight is under 185. However, the lightest I’ve been since I’ve stopped growing is 205, and that was when I was playing football (ie, lots of running), not doing significant weight training, and not eating enough to gain more weight. Beside the fact that I think it’s quite impossible for me to reach my ideal weight, even when I was 205, I felt like I looked WAY too thin and I feel like I look much better at an even higher weight. I couldn’t imagine losing ANOTHER 20 lbs on top of how thin I was then.
Granted, my weight isn’t fat, so it’s not exactly a fair comparison, but I can certainly agree with the concept that a BMI ideal weight isn’t necessarily a desirable state for everyone.
I’m adding to the sentiments that BMI isn’t at all a good calculator for health. It doesn’t take into account muscle vs. fat at all. I’m sure that the woman in the OP its obvious which was contributing to hers. For me though at my peak I was 5’9 and 185, thats my top weight and the best shape I was ever in, running <6 minute miles and lifting 3 times a week… BMI just isnt that great a calculator of actual body size or proportion (fat, obese, or what have you)
I definitely don’t propose this as a diagnosis to the woman in the OP, but it is relevant as an answer to the general question of whether there is a disorder that could make someone think they are too skinny. I think a better version of your face analogy would be someone with a normal face who thinks it looks ugly, and hides behind long, messy hair, or destroys her normal complection with excessive makeup due to imagined flaws.