SQL databases are not great at storing huge chunks to data (petabytes of video) but those are easily handled by the native filesystem. Just make sure the write access is safely wrapped in a DB transaction, RAII style. This works and scales well enough except for the failure mode: over stressed egress (typically SELECT queries) will starve ingest (a more or less constant load of UPDATE & INSERT queries).
At that point, you want to scale horizontally. As mentioned, replicating the SQL backend file over NFS or rsync is simply a horrible idea. Surprisingly we ultimately discovered that SQL-level replication did not solve the problem reliably either: scale improved, but the starvation failure mode (read locks blocking DB writes) persisted (be it less frequently).
The replication layer we needed was at the application level where it's much easier to express that actually we did not need the real-time coupling between media ingest and egress. Eventual consistency is good enough: if the system is about to collapse, simply fail by adding latency so you can always keep ingest healthy.
Worst case, people watching a popular sports event will see players buffering. Which is bad — don't get me wrong — but far better than a catastrophically blocked pipeline and congested video encoders.