I had another thought as I was confused why it worked on my first run-through and then didn’t on the lastest from today, so I spun up a brand new site as I think I used a fresh one the last time round - and this time discobot did appreciate my coconut link. 
I then belatedly remembered that safe mode existed…
And I tried it on my original test site with safe mode enabled, and requested a new tutorial, and this time he also liked my onebox as well. 
So I’m guessing it must be a conflict with a plugin or theme component. I do have quite a few of the official ones so it may be easier to look through the ones on the other site. I’ll keep digging. 
Update: No, now it just seems to work every time no matter what. 
@Moin, can you give me a specific set of repro steps where it consistently doesn’t work for you?