This is just incorrect
…or containers, e.g. Docker/Podman
Distrobox is a script that manages Docker/Podman containers
What you are installing can cause damage so IMHO it’s more about keeping things manageable while having your actually important data…
Programs are installed the container, not on the host system. When you break the container the host system is fine unless using rootful (or Docker) containers.
…while having your actually important data (not programs, downloaded content, etc but rather things you did yourself, e.g. written documents, sketches, configuration files, prototypes, photos, etc) safe…
Using Distrobox does NOT keep your own files safe, it actually mounts your home directory and external USB drives inside the containers by default fully exposing your documents to whatever you install inside.
From the documentation:
Isolation and sandboxing are not the main aims of the project, on the contrary it aims to tightly integrate the container with the host. The container will have complete access to your home, pen drive, and so on, so do not expect it to be highly sandboxed like a plain docker/podman container or a Flatpak.
It works well when you want to install software that is not compatible with your distro, but it is not a great security measure since it integrates with your host system instead of acting as a sandbox.