1. A computer-implemented method for firewalling in a multi-tenant distributed service, comprising: under control of one or more computer systems configured with executable instructions, provisioning a plurality of computing resources to a plurality of tenants of the multi-tenant distributed service responsive to user interaction with a provisioning user interface of the multi-tenant distributed service, the plurality of provisioned computing resources being maintained by the multi-tenant distributed service with a plurality of server computers of the multi-tenant distributed service; maintaining, with a firewalling component in a supervisory layer of the multi-tenant distributed service, a plurality of virtual firewalls that enforce a plurality of computing resource policy sets with respect to the plurality of provisioned computing resources, the plurality of computing resource policy sets that include firewalling policies established by a plurality of service users authorized by the plurality of tenants, the firewalling component being distinct from the plurality of provisioned computing resources; receiving, at a resource user interface of the multi-tenant distributed service, a first request targeting a distinguished computing resource of the plurality of provisioned computing resources; identifying, with the firewalling component in the supervisory layer of the multi-tenant distributed service, a distinguished virtual firewall of the plurality of virtual firewalls that enforces a distinguished policy set of the plurality of computing resource policy sets with respect to the distinguished computing resource; checking whether an update of the distinguished policy set is required based at least in part on information associated with the first request; and submitting a second request targeting the distinguished computing resource, with the firewalling component in the supervisory layer of the multi-tenant distributed service, to the distinguished virtual firewall to obtain enforcement of the distinguished policy set, the second request based at least in part on the first request.