The iPhone 5C in question uses an A6 processor. It encrypts data by comingling the passcode with the unique device ID to create a a strong 256-bit key, so you can't just pull and brute force the flash memory chip. Meanwhile the OS will wipe the key if you guess a wrong passcode too many times, making the data forever inaccessible.
However there is one vulnerability with the A6 that some have theorized.[1] If you could somehow get around the wiping part, you could keep guessing passcodes. A typical 4 or 6 digit passcode could be guessed in under a day. So it may be possible to copy the flash memory into a soldered-in test rig that is effectively wipe-proof. It would restore the contents every time it's wiped. So that's the best guess I know of for what happened here.
But starting with the A7 Apple added the secure enclave. This now enforces at the hardware level an escalating time delay with each wrong passcode guess. It goes all the way up to a one hour delay.[2] That's also where the (unreadable) unique device ID resides, so there's no swapping out the processor with a rig. The key is forever wedded to this protection against brute forcing.
That is pretty darn spiffy from a security standpoint. If it works as designed, about the only hope anyone has of getting at data from an A7 or later device is through iCloud backups.[3]
[1] https://www.aclu.org/blog/free-future/one-fbis-major-claims-... see also http://blog.cryptographyengineering.com/2014/10/why-cant-app...
[2] https://www.apple.com/business/docs/iOS_Security_Guide.pdf
[3] Either that or some kind of peek into the secure enclave. It's specifically designed to inhibit this at a hardware level, but perhaps a nation-state could figure it out (e.g. verrrrry carefully grinding it down without destroying it and looking at state with an electron microscope).