Here's another bike that I suspect has at least an Asian-produced frame: my 1987 Schwinn Cimarron.
These were said to have been made in Schwinn's Greeneville plant, but the SN doesn't line up with those shown in the long-running Cimarron thread, having only a single letter at the beginning. T-Mar's list suggests that a few different mfrs including Bridgestone produced bikes/frames for Schwinn, and this SN would line up with Bridgestone's system and a September 1986 build, very plausible.
I suspect the frames for these--at least at this date--were made in Asia then the bikes assembled in the US. They also have headbadge SNs, apparently recording the date the bike was finished, and the headbadge SN for this bike suggests it wasn't completed until mid 1987.