I filed the claim on December 31. It was received on January 4 (holiday got in the way), approved on January 12, and I got the return box on the 13th. The chair was picked up on the 14th, arrived on the 18th (weekend again), and shipped back out, repaired, on the 19th. It'll arrive tomorrow.
The time could have been a bit shorter, though the holidays were the big issue. OTOH, I will only have been without it for a week, and that's a lot better than the 12 business days they cite.
I am impressed with Herman Miller's approach to warranty claims. They don't quibble over the little stuff. I would not have been surprised to be told that the chair would be fixed, but not under warranty. Instead, once the claim was in, it all happened with little effort. They sent me a suitable box to ship it in, and even an Allen wrench to take the back off (the instructions were not to ship it unless it specifically needed repair). It all was done at no cost to me. That's how warranty work should be handled.