Thanks for your reply. As I live in Thailand, which does have some sort of tax treaty with the USA. The majority of people working in this region are doing so as teachers, either employed by a foreign school in the country in which they reside, or working online for Chinese or other companies.
None of those provide a W-2 or 1099-MISC to anyone. The are foreign companies. They couldn't care less about the USA or what the IRS requirements are.
I could declare my part-time online teaching income as self-employment income. It's less than $10k. My impression is that I could choose to pay Social Security/Medicare tax (and it might benefit me in terms of Soc. Sec.) but I did a run-through on TurboTax and wasn't required to pay. So, for the time being, I don't think I will.