Again, sites has nothing to do with the OTA aliases; it's done at the system level within Provisioning Manager on a subscriber basis. Specifically the Radio Capabilities Profile Security Group(s) must have the Radio Alias Update parameter set to enabled. If the system has only one Radio Capabilities Profile, then it applies to the entire system. If there are multiple Radio Capability Profiles (most likely the case), then the feature can be enabled individually for each profile, and thus would only apply to a subset of subscribers.
In your example, Elizabeth would need to have their own unique profile in order to enable OTA aliases (or be part of a profile that has the feature enabled). Of course this would need to be enabled by someone with access to Provisioning Manager and the ability to make changes to the Radio Capabilities Profile, which would most likely be the state themselves, not individual agencies.
Group Services is the APX subscriber feature that must be purchased in order to display the OTA aliases in the radios. If Elizabeth has Group Services in their APX radios and they enabled decoding of OTA aliases, they would see whatever the state provisioned to be encoded. In this case, console aliases.