1. An apparatus comprising: information technology infrastructure comprising: a computing environment shared by multiple tenants of a service provider; a secure assessment environment separate from the computing environment; an evidence collection module associated with the shared computing environment and configured to collect compliance evidence from the shared computing environment and to make the collected compliance evidence available to the secure assessment environment for storage therein; and a tenant assessment interface to the secure assessment environment configured to receive assessment requests from the multiple tenants and through which the multiple tenants can access the compliance evidence as stored in the secure assessment environment in a manner that does not undermine security of the shared computing environment; wherein the compliance evidence comprises information sufficient to allow a given one of the tenants to verify that the shared computing environment is configured in accordance with a specified security policy; and wherein the evidence collection module is further configured to collect the compliance evidence based at least in part on expected tenant assessment requests.