They've posted job ads for their data centers in the past that mention Solaris and IBM/AIX. I don't know if there's anything official beyond that.
They're known to use "Teradata" (i.e. Dell), "Oracle" (i.e. FKA Sun) & HP DL-series servers alongside NetApp storage. iTunes is reportedly one of the world's largest SAP installations and that'll almost certainly be on AIX or Solaris with Oracle databases on the aforementioned NetApp spindles. OS for other applications? Nothing stops Apple running OSX if they do the driver work, but honestly I'd walk in expecting a mix of Solaris, RHEL and Windows, like every other Enterprise(TM).
[ it'd be nice to think they run a lot of FreeBSD given their UNIX group's credentials but - correct me if I'm out of date here - the bge(4) issues of FreeBSD on HP Gen8 servers seem to undermine that ]
Separately, iCloud is reportedly running on Azure & AWS.
I think it's a pity that Apple abandoned the server market so completely, but I understand how a consumer-first strategy with a strong theme of "same experience everywhere" is antithetical to enterprise needs (specifically the demands of experience control & functional lockdown expected by corporate IT departments). I've done some hard yards inside large enterprises and seen first-hand just how wedded many CIOs are to the whole colossal Microsoft ecosystem; competing with that head-on would be a very long game.
Even if what you said were true, I don't know how it would be relevant. Darwin, which OS X is built upon is open source as well. Apple contributes to FreeBSD and it gave us clang. Hardly an example of a company that embraces closed source.
SPARC was interesting from a technical standpoint, but it wouldn't have been an asset to Apple. SPARC doesn't shine on low-end machines and they already had to ditch twice fancy CPU architectures. Internal servers? Hardly worth keeping a CPU division for when AMD64 works just fine.
Few people have a use for the ability to quickly move large files around the house. Media professionals, pirates with HTPCs... what else?
A few years ago, I remember some of their kernel engineers saying Apple's performance goals are holistic with their hardware ie prioritise things that the majority of their consumers (mainly low end laptops) would need. This seems reasonable, why invest in best of class IO when most users are on 54g wifi with a single 5400rpm HDD. The problem is now consumer hardware has caught up, gigabit wifi, PCI-e SSDs, 8+cores, retina screens, multi-level cache hierarchies.
One thing OSX does extremely well at is power management, and that's in a large part due to iOS. I wonder what Apple run at their data centers?