The CircleCI badge here shows as passing: https://github.com/coq/coq#coq
But the most recent commit in the (master) branch was actually failing: https://circleci.com/gh/coq/workflows/coq/tree/master
Given that we use the Workflow feature, may it be due to an absence of Workflow support in badges (the workflow as a whole failed because some builds failed, but the last build to finish in the workflow succeed and may have wrongly set the badge to passing).
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I have a similar issue, but in reverse. 
The badge shows failed, even though the latest scheduled workflow succeeded.
https://github.com/torokati44/inet/blob/integration/README.md
https://circleci.com/gh/torokati44/inet/33
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Possibly related? Status badge shows wrong status
I have a home-made dashboard of my 14 CircleCI project badges, and occasionally I have spotted one is wrong. It has not been enough of a problem for me to look into, and I wondered if browser caching may have contributed to it!
I have this happening right now, on a scheduled workflow. The badge is green when the build is very definitely failed. I am wondering whether the badge statuses are cached by last commit time, so changes that result of a scheduled build are not taken into account?