Major This wasn't manifesting in the browser, as my browser was automatically prefixing the url with a slash, but I finally confirmed it with plain ol curl
`curl http://ci.example.com/github-webhook/`
- result: same error about payload that you see in the browser
`curl curl http://ci.example.com/github-webhook`
- result: silence. no output.
I spent like 2 hours trying to figure this out, but mostly because I didn't realize that the github service "Update settings" button needed to be pushed before "Test Hook" would work. But that's an issue for github 
[JENKINS-17185] Trailing slash shouldn't be required for webhook url
`curl curl http://ci.example.com/github-webhook`
- result: silence. no output.
Is there no Location header redirecting to the expected URL?
Update: There is.
$ curl -i https://jenkins/github-webhook HTTP/1.1 302 Moved Temporarily … Location: https://jenkins/github-webhook/ … Content-Length: 0 Connection: keep-alive
So what's the problem here? Took me about a minute to figure this out.
This behavior in Stapler is deliberate, and changing it would result in lots of brokenness:
https://github.com/stapler/stapler/blob/master/core/src/main/java/org/kohsuke/stapler/Stapler.java#L715
This still appears to be an issue.
I experienced it with the Bitbucket plugin.
`http://server/bitbucket-hook` vs `http://server/bitbucket-hook/`
I checked the code for the Bitbucket plugin, and it does not appear that the problem lies there. As it doesn't appear they control URL matching.
I think this belongs in core.