Prospective employers can ask about WC claims after making an offer but before hire, if they ask the question of everyone in the same situation. See EEOC enforcement guidance here: Enforcement Guidance: Workers' Compensation and the ADA | U.S. Equal Employment Opportunity Commission
"Specifically, 4. When may an employer ask questions about an applicant’s
prior workers’ compensation claims or occupational injuries?
An employer may ask questions about an applicant's
prior workers’ compensation claims or occupational injuries after
it has made a conditional offer of employment, but before
employment has begun, as long as it asks the same questions of
all entering employees in the same job category."
Asking this type of question is going to be more prevalent in some industries than others. Discrimination based on the answer would be illegal, except to the extent that the answer, or a subsequent medical exam, revealed a medical condition that prevented the employee from doing the job.
HIPAA also seems to have some special provisions around WC that lessen protection of the claimant’s privacy: http://www.wcb.state.ny.us/content/main/SelfInsureds/HIPAAInfo_SIEmp.jsp
I do agree that WC is one possibility, but your post seems to overstate the privacy protections. If your location is in CA, maybe CA has stronger state privacy laws?