I was at Apple for almost ten years. While I was there I was able to see how Apple handled internal servers (and employees launching internal tools) for multiple departments. I can’t claim comprehensive knowledge, only anecdata on what I saw.
Apple had an internal group which handled the majority of back-end services; these services were run professionally by Apple’s admin team. This covered internal services such as authentication, web services, company wikis, and more. I have no information on how these large internal and external services were run.
A counterpoint to company-wide services were services launched by employees for their peers – adding a group-wide internal chat or a log symbolicator for escalation engineers to read crash dumps. These services would almost always be run on a spare machine on an employee’s desk and almost never received professional support. I interviewed for a Sysadmin job for a large divison of Apple (large enough to have an executive on the Bios page). I was told the servers needed to be organized, as they were currently a motley collection of Macs collected from employees who had set up servers as needed.
I’ve heard that employees can use Google’s cloud internally; they would naturally develop stuff like Gmail directly in the cloud and using Google’s services natively. As stuff gets bigger, it can be scaled more easily since it started in the cloud. If something like iCloud sync started under someone’s desk as a bright idea could that be part of why it’s not scaling better?
This is likely completely wrong…but every time I hear about iCloud issues or concerns I’m reminded of a room with random Macs running an important part of Apple.