I think you are right on J-20 but the history of Saudi Arabia and China makes this at least a possibilty.
In terms of strategic value, an ICBM is even more important than a stealth fighter.
Granted the original transfer was in 2007 and President Bush himself had okayed it.
The real question is why are we only hearing about it now.
foreignpolicy.com
But that was an off the shelf sale and today China is helping SA build their own ICBMs.
US intelligence agencies have concluded that China has transferred missile technology to Saudi Arabia to help the desert kingdom build its own ballistic missiles in addition to the actual missiles it has bought from Beijing in the past, CNN reported on Thursday, citing sources. Several US...
eurasiantimes.com
SA has strategic value that cannot be understated. So there might be a chance and we won't find out until much later.
In general, you are right. FC-31 is the one offered for export not J-20.