Skimming the health department web sites of various counties, it doesn't look like it. Most of them just provide the basic cases and deaths numbers. Whoever compiled this at the Stanford Open Data site (https://opendata.stanforddaily.com/#/datasets/covid19_bayare...) might be doing so manually.

SF County - https://www.sfdph.org/dph/alerts/coronavirus.asp

San Mateo County - https://www.smchealth.org/coronavirus

Alameda County excluding Berkeley - http://www.acphd.org/2019-ncov.aspx

Berkeley - https://www.cityofberkeley.info/coronavirus/

Santa Clara County - https://www.sccgov.org/sites/phd/DiseaseInformation/novel-co...

Marin County has an (ominously named) dashboard - https://coronavirus.marinhhs.org/surveillance