This is not true or at the very least confusing

https://www.postgresql.org/docs/current/backup-file.html says
"The database server *must* be shut down in order to get a usable backup."

Note: must is in italics.

Then we have section 25.3.3.1. Making A Non-Exclusive Low-Level Backup
which contradicts this statement with "Perform the backup, using any
convenient file-system-backup tool such as tar or cpio (not pg_dump or
pg_dumpall). It is neither necessary nor desirable to stop normal operation
of the database while you do this."

While I understand this is a complex topic. I think at the very least we
can refer to section 25.3.3.1 in section 25.2. I also think that the
discussion about frozen snapshots is ill advised. If I were doing it I
would use pg_start_backup before using any file system snapshot.

Regards,
Dave Cramer