* From the conversations I've had with cryptographers, there does seem to be a sort of consensus that Joux's DLP work is unlikely to result in a viable attack on RSA any time soon, or, for that matter, on any mainstream DLP scheme.
* But: that isn't a uniformly held opinion. Dan Boneh is an example of someone who seems to believe the line of research Joux is pursuing is going to harm RSA "sooner" rather than "later".
* As you note: RSA isn't looking sturdy today. I think the RC4 example is a good one. The recent attacks on RC4 weren't based on a newly discovered vulnerability, but rather on a more diligent effort to exploit an old one. I'm not convinced that there was any better reason for those attacks being unveiled in 2013 than that nobody had a strong reason to investigate them.
* A (just say) 10-year time scale is still relatively short! If we can reasonably predict material weaknesses in a cryptosystem 10 years out, we should replace it now. We don't generally choose to work with cryptosystems that offer us a margin of just 10 years to work with.
Finally, and most importantly: please understand that the audience at Black Hat isn't cryptographically literate. There are a couple crypto people that show up every year, but the attendees at Black Hat generally bring very little background in the subject with them. So, I think there's value in distilling subtle messages down to actionable information for that audience. A subset of the people in the audience at Black Hat are at some point going to try to develop their own cryptosystems, and they're much more likely to do that by trying to hack together RSA than they are ECC. The less attractive RSA looks to them, the better.
Thanks again for the corrective comment, though. I sort of wish Tom and Javed could have had you up on stage debating them. :)