Suppose there is a town with just one public IaaS cloud provider, and that every business in the town runs their own IT: some by hosting it on-premises, some by running it in the cloud. It seems reasonable to imagine that the cloud provider obeys the following rule: it runs IT for all and only those businesses that do not run their IT on-premises.
Under this scenario, we can ask the following question: is cloud provider's own IT in the cloud or on-premises? (remember that the cloud provider itself is also a business)
Of course this “faux” paradox is not a paradox at all. As I suggested on Twitter, “if you build a cloud, to your customers it will indeed look like a cloud; but to you it will look like a regular datacenter.”