When cloning a Registered Service, or RS, from one ArcGIS Organization to another, it will still point to the original source for the underlying data. Support sometimes gets questions about why this occurs, and this article provides an explanation.
A registered service is a pointer or reference to a set of data used to populate a map layer. That information may be in your ArcGIS Organization, or it may come from elsewhere. Since a RS is just a pointer, when you clone it, it will still point to the same reference. This is because, when performing operations in Backup My Org (BMO), you only have the ability to perform operations on content in your ArcGIS Organization. If you tried to clone a RS that pointed to a source outside your organization and its source, the operation would fail because you don't have permission to clone the source. Because there is a possibility a RS could rely on data from outside your ArcGIS Organization, Esri does not provide enough information about the registered service’s data source to clone it as well.
Think of it like this - your ArcGIS Organization is an encyclopedia. The Registered Service is an entry in the encyclopedia that cites a table. That citation could point to a table in another publication altogether (different encyclopedia, scientific journal, etc.).
Note: If the “table” is in the appendix of the encyclopedia, this would be analogous to when a Hosted Map Service has its service definition attached because they are both in the same book.
When you are cloning content from your ArcGIS Organization, you are making a new encyclopedia, using information from your current one. There are two different books, but you're copying info from one to the other. If you copy an entry that cites a table and the table is in your encyclopedia, you have all the necessary information to copy everything over to your new encyclopedia (how cloning most items works). If the entry cites a table in another publication, you can only copy the reference to that publication. You don't have permission to copy the other book.
Again, note that Esri does not provide enough information about Registered Services to determine if the table is in the appendix or another book. It treats every Registered Service as if the table is in another book. This is why, when you clone your RS from one ArcGIS Organization to another, it still points back to the original source - even if the service’s URL is in the first ArcGIS Organization.
Hopefully, this explanation helps you understand what's going on when Backup My Org clones a Registered Service.