If you paid close attention, you’ll notice the ‘DomainAdmin’ portion of that name. Yep, you got it right… they were running SSRS under the domain admin account. The Windows guy thought that it would be too much trouble to manage the permissions and get everything right on all the shares and DBs that it needed to access.
So this is when I pretty much lost it. These guys were running SSRS under a domain admin account because they were too lazy to do the right thing. It’s unthinkable. There may be some reasonable excuses why you’re not able to change your current security model to something better. You may even be able to convince me that you’re not just being lazy. But to actively be lazy about your security isn’t something I’m going to take lying down. Hey, I know it’s your shop, and I know you can ultimately do whatever you like, but I’m going to make sure you know what you’re doing.
Your SQL Server (and related) service accounts should not be Domain Admin. Period. This isn’t one of those “Well, it depends…” types of scenarios; there is no reason ever to use an account with Domain Admin rights as a SQL Server service account, and it is security malpractice to do so.