An "integrity assessment" is a paper "polygraph" test -- the goal of which is to determine your likelihood of engaging in conduct that would damage the employer. See this link
for an example. Typically, this type of test is used in retail sales positions, or banking, investment, etc., where persons work with product inventory, cash tills and/or other people's money. I don't know how useful it would be in a human resources position, since it would be pretty difficult for an HR manager to steal from the employer's 401(k) plans.
But, if there was a coincidence between the use of the exam and the offer withdrawal, then maybe the test picked up something that the employer didn't like.
Concerning your right to review the test, there is no right to do so, absent a legal action -- though the DFEH can review the test results,via an administrative subpoena, and it could have you take the test again and compare results to see if the results provided to DFEH were manipulated in some manner.
Concerning the reliabiltiy and validity, the legal requirement for any test is that it does not discriminate based upon race, color, creed, nationality, ancestry, religion, sex, sexual orientation, pregnancy, age or disability. Once again, were the test proved to contain unlawful discriminatory questions, then that could be evidence for a discrimination action. But, it would be your burden (or, DFEH's) to prove that the test is not a general and neutral test of secular ethical conduct. And, these tests are carefully written to avoid the possibility of violating the federal and state civil rights acts.
Hope this helps.