So this is really just here for my future reference, but it may be useful for someone else with the same issue. :D
Jenkins S3 publisher plugin was showing this error in Manage Jenkins - > Configure System -> Amazon S3 profiles:
"Can't connect to s3 service: unable to execute http request: peer not authenticated"
OpenJDK has different cert settings out of box than Sun JDK does.
Solution for my server:
Install Sun JDK latest version (1.8_40 in my case).