It's entirely possible to write a disk interface that is fully tolerant of losing power at any point in the access to the disk and not having "bad things" happen to the disk, disk structure, disk contents, etc. It's even possible to write the disk interface so the amount of data lost by a power loss is minimal. I have written several disk interfaces of this type myself. While I have no definitive knowledge of how TiVo interface is implemented, it seems quite reasonable to assume it will handle power failure "gracefully".
The only "problem" is that doing things this way is somewhat inefficient, so "high performance" disk access (ie PCs) usually opt for the faster, more responsive implementation, even though it does require buffers be flushed before power down or some structures can become "dirty".
Bottom line - quite trying to shut it down like a PC (can't be down) and just "pull the plug".