I think, that's the expected behaviour. As a teacher it should be possible to attempt a quiz without using SEB.
In the meantime a made some further investigations and tried the option "Yes - upload my own config" for SEB. I followed the instructions on https://docs.moodle.org/39/en/Safe_Exam_Browser saying that you have to redownload the config file, open it in the configuration tool of SEB (v3.0.1) and then copy back the displayed browser exam key to the moodle page. But still then the message " The config key or browser key could not be validated ..." remains. Very confusing.