Kind of, except that ETC itself has also done a hard fork to do major protocol changes, so it's not exactly right to call it the "original, unforked chain."
The original Ethereum Homestead blockchain was designed to demand at least one hard fork. The mining difficulty was set to increase exponentially after some time, in order to force the community to make a decision regarding switching away from proof-of-work toward proof-of-stake. The ETC community hard forked the Homestead chain to remove this "difficulty bomb."
That's quite different from the "TheDAO" hard fork, but it's still a hard fork of a blockchain, so it's not true that ETC represents completely immutable law -- that community can also demonstrably agree to hard fork.
The original Ethereum Homestead blockchain was designed to demand at least one hard fork. The mining difficulty was set to increase exponentially after some time, in order to force the community to make a decision regarding switching away from proof-of-work toward proof-of-stake. The ETC community hard forked the Homestead chain to remove this "difficulty bomb."
That's quite different from the "TheDAO" hard fork, but it's still a hard fork of a blockchain, so it's not true that ETC represents completely immutable law -- that community can also demonstrably agree to hard fork.