I tested positive/treated for strep 5x (rsat), little/no symptoms. Last test was positive, culture was negative. What causes false positive results?

Latent infection? Some people have recurrent MRSA (multiply-resistant strep aureus) infections that are treated successfully and recur. There is a possibility that they (or you) could be harboring strep in your nose. The sinuses don't have great blood flow, and so may potentially "hide" bacteria. This could explain your odd results. Put bactroban (mupirocin) up your nose daily as a preventive measure, and see what happens.
Strep carrier. 10-15% of people carry strep without symptoms. So a throat culture regardless of throat symptoms will be positive. Really only relevant if you are having recurrent severe tonsillitis ( fever >102, and missing days of work or school with each episode) or the rare situation where others strep illnesses can be traced back to you.