Property management is a high risk area for litigation. Typical claims include bodily injury/property damage (which is excluded from a lot of E&O policies, but can be added by endorsement through some companies), wrongful entry, wrongful eviction, libel/slander, discrimination, violation of fiduciary duty, failure to renew contracts/leases and on and on.
Ultimately, in most states, the broker is responsible for ALL actions performed by their agents through vicarious liability. Her concerns are legitimate, but a proper risk management plan can help alleviate some of the risk involved.