Host filesystem manipulation from docker vs. virtual machine

When reading about docker, I found a part of the documentation describing the attack surface of the docker daemon. From what I was able to understand, part of the argument is that it is possible to share (basically arbitrary) parts of the host filesystem with the container, which can then be manipulated by a privileged user in the container. This seems to be used as an argument against granting unprivileged users direct access to the docker daemon (see also this Security SE answer).

Would the same be possible from a virtual machine, e.g. in VirtualBox, which on the host is run as an unprivileged user?

A quick test where I was trying to read /etc/sudoers on a Linux Host from a Linux guest running in VirtualBox did produce a permission error, but I would not consider myself an expert in that regard in any way nor was the testing very exhaustive.