How can I read a file on the host from within a privileged container?

I can't mount any volumes as I do not control how the container is created, but I can at least request a container in privileged mode. That should be good enough to read a file on the host, right? But what would I have to do?

TL;DR

I am running Concourse (CI/CD tool) in a Kubernetes cluster, but unfortunately it is not deploying its jobs as regular Kubernetes pods, but as Garden containers.

My problem is that I need to access the default Kubernetes service to interact with the hosting cluster (every pod can), but I can't do that from within a spawned (nested) Garden container without the token that is mounted in the pod that is running Concourse. The only configuration option is to make the (nested) Garden container privileged.

So, how can I read a file on the host from within a privileged container?

I can't mount any volumes as I do not control how the container is created, but I can at least request a container in privileged mode. That should be good enough to read a file on the host (i.e. in the pod, since the Garden container is nested inside the pod container), right? But what would I have to do?

Thanks in advance!