I don't have any first-hand experience in getting milked 200 USD per day in Bhutan (which is discounted to 100 USD from 01 September 2023 to 31 August 2027), but I see Europeans leaving reviews in those Airbnb and https://www.mfa.gov.bt/rbedhaka/visa-for-visiting-bhutan/ and https://visit.doi.gov.bt/help/faq don't say that being part of an organized tour is required to get a visa, which makes sense as tourists can stay up to 90 days in Bhutan (which would be a rather long organized tour). Therefore, I'm inferring that the information you have read is outdated.
From https://visit.doi.gov.bt/help/faq:
- Visitors can apply for their visa or permit through this website, or they can engage tourism service providers to process their visa or permit.
- Foreigners can stay in Bhutan as a tourist for a maximum of 90 days.
I've posted a list of current requirements to get a tourist visa in Bhutan here.