Update:
Another Win2012/R620 exhibits the same behavior. I didn't think so at first, because this actually looks fine in OME, but like the first server it fails the SNMP-test.
So I suspect that the info shown in OME is old news from OMEs database.
Common between the two servers: They are both running the Hyper-V role, and I suspect that may be the culprit, since the server for which I can see some information in OME only recently had Hyper-V activated, while the first server has been running Hyper-V for a long time.
We have other Hyper-V servers which work fine, but they are 2008 R2.