Yes, or NVRAM, exactly as step 1 in my scenario mentions.
The problem is that the disks they're managing don't. (EDIT: barring SSDs with supercaps, but that's an entirely other discussion.)
If a write has been accepted by the disk and acknowledged as written — but in reality has only been stored in the disk's on-board cache — and you suffer a power loss before the write can be flushed to permanent storage (be it spinning rust or NAND cells), then you have lost that data.
This is exactly why a RAID controller worth using will disable a drive's onboard cache. Because disks lie.
