In the great Google infrastructure, I'm sure that Google knows what IP address your site is hosted on, and all the ones tied to it. In one of the past MOZ blog posts you can see a number of factors Google looks at to see what you control. We used dedicated IP's for each client, just in case anything ever happened to one account, it would not affect the others. They are close in IP address range, since they are on the same block, but none are on the same number. This isn't an attempt to gain SEO rank, as much as it is to protect the client.
Locally, I have reason to believe its a different story. For example, we are located in St Louis, and use a local server center located in downtown St Louis. After changing our site from hostgator under a shared IP, (Provo, Utah) to a local server center, we saw an drastic (in internet time) improvement in site load time, responsiveness, and believe it or not, a ranking boost....true story, no joke. It wasn't a large boost, but we moved up 2 spots on our main keyword on page one, and 1-2 in other places. We didn't make any other changes to the site, other than adding a few blog posts, and this was not around any major algorithm shift or update. We have seen this pattern repeat with other clients as well.
My guess is that Google liked the decreased load times, the local server location (as it matched the city on our site, somehow verifying our location further), and the fact that the site was on a dedicated IP address. If we had just changed the site's IP address by itself, I do not think we would have seen any impact or result change.
"there is really no SEO benefit of having a unique IP for each of your sites unless you're attempting to pass link juice between each, which falls into the greyhat category."
I don't think you would get away with this for very long, or that it would benefit you in any way. Google would see that you host or control these sites through your analytics account, or IP range. If you wanted to pull it off, and have separate analytics accounts, dedicated IP's etc, I doubt the result would be worth the time.