Facebook maintains it's own fork [0] of MySQL. A couple of interesting talks are also available: MySQL at Facebook, Current and Future [1] and Massively Distributed Backup at Facebook Scale [2].
[0] https://github.com/facebook/mysql-5.6
[0] https://github.com/facebook/mysql-5.6
And yes, MySQL has a lot of problems, but it seems to be better for "seat of the pants" usage (that is, when you don't need too many SQL capabilities and wants to use it mostly as a data store)
It really put me off ever wanting to even consider working at Facebook.
Digging around I can't find either the blog or video :(
The problem with making absolute statements about what FB does is that it seems to be structured as a large number of mostly independent teams that are free to choose and develop whatever technology they need to solve their problems. There's actually a talk about scaling by a FB dev (don't have the link right now) that uses this as an example for what it means when they talk about "Facebook scale" (another example is that their monorepo outgrew git so they created their own extension to mercurial instead).
It's entirely possible that the main use of MySQL at FB is as a key-value store while at the same time there are small parts of applications using it with plain old queries and joins.