Appreciate all the responses. Yes I'm American for those concerned. I don't see the benefit of 100% ownership of the company. I highly doubt I'd make anything near the Foreign Earned Income Exclusion limits for US taxes so anything I make would essentially be tax-free on my US taxes anyway.
I know dozens of foreign dive instructors in Phuket who are freelance instructors who coordinate with Thai accounting firms to process tax, employment, etc. payments so they can obtain/maintain a non-B visa and work permit. My understanding is that these instructors have essentially created Thai companies, since I always hear that there's a requirement of 4 Thai employees, presumably so that I'd get one foreigner work permit quota.
All I'm asking is whether that sort of company would allow real estate purchase.
I suspect the answer is "it depends", based on the answer provided by @Maestro.
Thanks for everyone's responses!