I don't know BGP well, but it seems easier for peers to just drop FB's packets on the floor than deal with a DNS stampede.
How would a few bytes over a couple of UDP packets for DNS have any meaningful impact on anyone's network? If anything, things fail faster, so, there's less data to transmit.
For example, I often use ordns.he.net as an open recursive resolver. They use PowerDNS as their software. PowerDNS has the default of packetcache-servfail-ttl of 60s. OTOH, fb.com A response currently has a TTL of 300s — 5 minutes. So, basically, FB's DNS is cached for roughly the same time whether or not they're actually online.
If your network cannot accommodate another network's DNS servers being unreachable, the problem is your network, not the fact that the other network is unreachable.
A network being unreachable is a normal thing. It has been widely advocated by DJB (http://cr.yp.to/djbdns/third-party.html) and others, since decades ago, that it's pointless and counterproductive for single-site operators to have redundant DNS, so, it's time to fix your software if decades later somehow it still makes the assumption that all DNS is redundant and always available.
I didn't notice any slowdowns on Monday, BTW. I don't quite understand why a well written DNS recursive cache software would even have any, when it's literally just a couple of domains and a few FQDNs that were at stake for this outage. How will such software handle a real outage of a whole backbone with thousands of disjoint nameservers, all with different names and IP addresses?