Copy protection schemes behaved kinda wonky on the Beta format, so its usually less of a problem dubbing from Beta than from VHS (which was much more consistent with CP and more difficult to dub from).
DVD/HDD recorders don't have any grey area: if they allow the dub to proceed, it usually means the CP has been ignored or bypassed and the HDD title should dub freely to DVD. If a recorder was sensing any kind of CP, it would usually not allow you to dub the tape at all.
But every now and then, you can encounter a weird technical glitch or interaction which doesn't make any sense, as happened with this tape. Most likely, your DVD/HDD unit permitted the dub because it didn't sense copy protection in the usual way, but after you pressed "stop" and the HDD file system analyzed the title, the recorder mistook something in the video as being the broadcast "copy-once" protection signal. This allows recording to HDD but not dubbing a copy to DVD.
Another possibility is a corrupt sector on the HDD which is interfering with the status of the title. I have had this come up several times recently on my oldest recorder. The solution for me was to change the thumbnail, change the name, change the chapters, whatever I could to get around the bad sector. Almost always I can then make a DVD, but sometimes not. In that case I delete the title and do the recording all over again.
Odds are if you do this particular dub over again, it will work correctly. If not, something embedded in that Beta tape is definitely bothering your DVD/HDD recorder and you will need to try a CP filter box or TBC wired between the Betamax and your recorder.