We have added Referrer to the parameters collected when the widget API is invoked: viewable via My API Log when logged in to the API Platform Control Panel. You can view on which pages on any given domain the API was called. This is especially valuable if you use the API widget on multiple pages (entry points).
Note that referrer will be undefined if the user has configured their browser to not send referrer header. However, such an incidence should be rare. However, at a later date, we may look at offering the option to hardcode referrer as a API option: which would override dynamic referrer detection.