When cloning a Registered Map Service, or RMS, from one ArcGIS Organization to another, it will (most often) still point to the original source for the service definition. Support sometimes gets questions about why this occurs, and this article provides an explanation.
A registered map 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 RMS is just a pointer, when you clone it, it will still point to the same reference. This is because, when performing operations in BackupMyOrg (BMO), you only have the ability to perform operations on content in your ArcGIS Organization. If you tried to clone a RMS 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.
If you have the source service definition attached to the service, you will be able to clone both. This is because this attachment lets your ArcGIS Organization know you have the appropriate permissions to perform operations on both the RMS and its data source, and it is able to inform BMO that you have those permissions.
Think of it like this - your ArcGIS Organization is an encyclopedia. The Registered Map 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.), or it could point to a table in the appendix of the encyclopedia. In the second case, the table is "attached" to the entry because they are in the same book. This is analogous to when a source service definition is attached to a RMS.
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. 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.
This is why, when you clone your RMS from one ArcGIS Organization to another, it still points back to the original source. The only way for you to get around this is if the RMS is published with its source service definition attached. Only then will your ArcGIS Organization have enough information in order to tell BMO that you have the right permissions to clone everything.
Hopefully, this explanation helps you understand what's going on when BackupMyOrg clones a Registered Map Service.