https://github.com/matrix-org/synapse/runs/4067253219?check_suite_focus=true had this test fail in 1/6 sytest runs.

I wondered if the changes in #1160 had unintentionally introduced some kind of flakey problem. But the failure in that link does not arise from running sytest on synapse with workers (the usual suspect for for flakiness). That was a surprise.

Raising this so we can track any future sightings.