I'm still confused, because I seem unable to find a lot of rules quoted here.
On p. 247 it says that a host has a rating of 1-12 and matrix attributes derived from that. All ICs running on the host have exactly these attributes. But if a host needs to role against a decker's martix action, it needs to have not only matrix attributes, but mental attributes as well. Of course it also has its host rating.
Also, hosts do have owners as stated on several occasions (p. 236-237 also p. 218; 219; 221 or the IC "Track" p. 249); hell, even grids have owners (p. 215 and p. 236-237). In fact it seems to run like this: You buy a device or anything running in the matrix, you will receive the rights as an owner, but owning a device (legally) and being the owner (matrix rights) isn't necessarily the same (p. 236).
Transferring matrix owner rights takes about one minute and is necessary to avoid that the item behaves like someone else's property all the time (p. 247).
Some matrix actions call for rolls vs device rating. In this case I guess device rating is substituted by host rating, making data bombs on files in high rated hosts very mean. But if you're trying to spoof command (p. 242), you have to go against Logic + Firewall, not device rating + firewall, since you're working against the capability of the owner to simulate his work, so that the host/device thinks you are in fact him.
So I guess I'll need to create an owner for eacht device after all...