I think you are mixing two different concepts with each other and possibly even more.
The feature of index/table partitioning is explained in the following document:
Reference: Partitioned Table and Index Concepts (Microsoft Docs)
In short ...
SQL Server supports table and index partitioning. The data of partitioned tables and indexes is divided into units that can be spread across more than one filegroup in a database. The data is partitioned horizontally, so that groups of rows are mapped into individual partitions. All partitions of a single index or table must reside in the same database. The table or index is treated as a single logical entity when queries or updates are performed on the data.
...and listed under the Benefits of Partitioning:
You can transfer or access subsets of data quickly and efficiently, while maintaining the integrity of a data collection. For example, an operation such as loading data from an OLTP to an OLAP system takes only seconds, instead of the minutes and hours the operation takes when the data is not partitioned.
This section might be leading you to believe that you could load lots of data faster into your centralised DEV database with backup/restore. However, this is only valid if you are talking about a data transfer and is not valid for a backup/restore scenario. Explanation follows in the Summary.
Files and Filegroups
Then you have the features encompassing Files and Filegroups which is explained in the following article:
Reference: Database Files and Filegroups (Microsoft Docs)
At a minimum, every SQL Server database has two operating system files: a data file and a log file. Data files contain data and objects such as tables, indexes, stored procedures, and views. Log files contain the information that is required to recover all transactions in the database. Data files can be grouped together in filegroups for allocation and administration purposes.
I won't go into further details here but instead carry on with the summary.
The whole database is split over the filegroups used for partitioning. It is true that the one filegroup may contain data for only one table partition (e.g. a single customer), but it is logically linked to the other filegroups split over the various *.mdf and *.ndf data files.
Restoring a single filegroup would require a roll-forward of all transaction log backups to bring the database back to a consistent state as discussed in the following article:
Reference: How to: Restore Files and Filegroups (Transact-SQL)
The transaction log backups, if applied, must cover the time when the files and filegroups were backed up until the end of log (unless ALL database files are restored).
This would however require you to restore the "Customer's FILEGROUP" (as per your idea) to a consistent state, which would include all the data (..in the transcastion logs...) for all the customers, because otherwise the database would be in an inconsistent state.
So partitioning data does not simplify a backup/restore scenario. You have to have the whole database in order to restore a specific filegroupd, but then you need all the transaction logs to ensure a consistent database.
In the end you have the whole database and nothing but the whole database.
Ha, but you quoted...
You can transfer or access subsets of data quickly and efficiently...
...but only on a data level. You can dump the contents of the partitioned table to a CSV file for future import into an adequate table, or start a data transfer between two databases (OLTP and OLAP) as can be seen from above original quote:
For example, an operation such as loading data from an OLTP to an OLAP system takes only seconds, instead of the minutes and hours the operation takes when the data is not partitioned
..but does this then contain all the (referential) data required to have a consistent data set? Presumably not.