Bill's argument is indeed correct. Both copy-on-write and log-structured storage systems eschew in-place updates/writes. Both instead choose to write the new data in a new location and update the pointer to the data to point to the newly written location. Updating the pointer required another write, which is again done out-of-place. This leads to a trickle of out-of-place writes leading to the root of the metadata. Both log-structured and copy-on-write storage organizations use this style of updates. The only difference between them is that log-structured storage systems enforce the location of the new writes to be contiguous (to benefit from superior sequential write performance of storage devices) whereas copy-on-write.

The LFS and WAFL file system papers are good references to learn more about log-structured and copy-on-write file systems. And if you want a lighter read than the papers, my summaries of LFS and WAFL are not too bad either ;).