"Carolyn Wang, communications lead for Verily, told The Verge that the “triage website” was initially only going to be made available to health care workers instead of the general public. Now that it has been announced the way it was, however, anybody will be able to visit it, she said. But the tool will only be able to direct people to “pilot sites” for testing in the Bay Area, though Wang says Verily hopes to expand it beyond California “over time.”"
From https://www.theverge.com/2020/3/13/21179118/google-coronavir...
From this quote and the behavior of Google's communications team (whether Google or Verily), you can assume that Google/Verily were caught off guard by the announcement of Google's involvement. Whether it was Google's original intent or not, it seems Google is trying to make the best of the situation now.