Hey Walter, there may be another explanation for what happened here.
Some years ago I visited a bird banding station. The head bander placed a small bird on its back. The bird layed perfectly still. The bander explained that it remained still because birds do not lay on their backs, so finding itself in an unfamiliar position it did not know what to do.
In this case I'm wondering if during the "fight" with the other sparrow it somehow found itself hanging upside down. Being in an unfamiliar position, it did not know what to do and so remained still until another sparrow dislodged it.