The current version of GA Connector doesn’t actually use Google Analytics API to populate CRM fields with analytics data (source, medium etc). Instead, GA Connector emulates Google Analytics tracking algorithm precisely.
We took this approach because it allows more flexibility and it works faster this way.
The product is still called GA Connector because it uses Google Analytics algorithm to track information and because it also sends CRM data to Google Analytics (for a limited number of CRMs only though).