Apple does operate its own infrastructure. It has numerous, exceptionally large data centers in the USA, Europe and China. Most notable is the $1 billion, 500,000 square foot facility in Maiden, North Carolina.

Apple probably augments their own infrastructure with cloud providers for various reasons, e.g. increasing geographic diversity, allowing for progressive growth, and to handle comparatively small jobs (e.g. merely a few hundred VMs).

I imagine it would also be a waste of Apple's time to tool up their own data centers to offer general purpose cloud computing services.