If you are updating the parent table and the partition key is correctly defined, then an update that puts a row in a different partition is translated into a delete on the original child table and an insert on the new child table, since v11 IIRC. But this can lead to some weird results if you're using multiple inheritance so, well, don't.

I believe they were just pointing out that Postgres doesn't do in-place updates, so every update (with or without partitions) is a write followed by marking the previous tuple deleted so it can get vacuumed.