investigators surveyed women and asked them whether they had ever tried to end a pregnancy outside a clinical setting, or if their best friend had.
The question is "ever," not in the past five years. 100,000 would be about 1.5% of Texas women in the 18-49 age group (30 million Texans, 50% female, about 45% 18-49), which sounds plausible. Presumably, almost all of these women or their best friends attempted a self-induced abortion before the law changed in 2014, so it doesn't make much sense to draw any public policy conclusions about the change in the law.
It's also unexplained how they analyzed the data. The question is whether a woman or her best friend had even done something. E.g. If 1 woman in 100 answers "yes," does that mean that 1 woman in 100 attempted a self-induced abortion, or 1 woman in 200? Presumably the second. But that could produce an overcount since it's not at all clear whether "best friend" refers to one person, or a whole bunch. It could produce an undercount since a woman would not necessarily know whether her best friend had ever attempted a self-induced abortion, and because if both a woman and her best friend had done this it counts as one "yes." Also, some women may not consider themselves to have a female "best friend."
I'd assume that the best friend language was actually an attempt to work around what would otherwise be a systematic undercount: if you ask every woman in TX (or anywhere) if they'd ever self-induced, then there is literally no chance of capturing every incident. Add the "best friend", and now you get women who talk about themselves with "BF" as a screen as well as women who won't speak for themselves, but have an IRL BF report.
Your point stands that you can't treat the resultant number as 1:1 with reality, but I don't think it's anything like 1:200, and was never intended to be.
I have no idea how you'd develop a robust model for how to convert it, though.
I have a friend who studied survey research in graduate school. He doesn't know that area specifically, but he says the "best friend" is 95% a way to get people to talk about themselves.
Based on 4, I'd say I'm about 2/3 of the way to a Masters in survey research.
The rest is math and being hit over the head with a Kahneman and Tversky book.
98% of people who studied survey research in graduate school are best friends with Moby.