A solution, of sorts...
My colleague found that selecting the link and clicking on 'prevent auto linking' in the toolbar changed the auto-embedded clip into a plain link, which showed up as expected in the forum email message.
(button with the chain link with red cross over it)
I'd prefer if the default behaviour was the opposite, ie insert the normal link and require the extra click to convert to an embedded video. But at least its a solution!
Maybe this will help someone else who has been frustrated by this feature?