These things can pump out 12Gbit during peak viewing, which is enough for about 4,000 avg. 3 Mbit streams.
If they can cram in 256GB of DRAM, that's enough room for a 64MB buffer per stream, or about 170 seconds worth of streaming. Now you only need to be able to fill those buffers at a rate of about 24/second.
I'm assuming whatever file system is on the disks uses a massive block size, so the number of seeks you'd have to perform to pull 64MB off is probably pretty low. Eight? Sixteen? Even if it's the latter, that's only 384 seeks/second, which you could very plausibly do striped over only a half dozen disks, and the device presumably has many more.
If they can cram in 256GB of DRAM, that's enough room for a 64MB buffer per stream, or about 170 seconds worth of streaming. Now you only need to be able to fill those buffers at a rate of about 24/second.
I'm assuming whatever file system is on the disks uses a massive block size, so the number of seeks you'd have to perform to pull 64MB off is probably pretty low. Eight? Sixteen? Even if it's the latter, that's only 384 seeks/second, which you could very plausibly do striped over only a half dozen disks, and the device presumably has many more.