This is a known issue with OAM publish. I filed a bug about this internally a couple of weeks ago, and it's being looked at now.
It would be hugely helpful if this info was posted on the forum, I have looked and searched much of the day for other postings to no avail.
Presumably this is the same problem that stops the JS folder being saved to the web folder - not to mention the font folder if one has been created for a custom font offline.
Don't recall there being a bug report list as per DPS, but happy to be told otherwise. Many thanks for the responses. Very much appreciated.
I'm working on getting it into our known issues list so that the confusion won't come up while we're looking at it. Stay tuned...