Can a CEO have personal values that conflict with the values promoted by the organization and still be an effective ethical leader for the organization?

LA 1: 
NEWS RELEASE:  Mar. 31, 2014. The makers of the popular web browser Firefox, is facing a media firestorm in protest of their recent promotion of Brendan Eich to CEO. Eich was an internal promotion for the company, having been CEO since 2005, but it’s Eich’s $1000 contribution to the 2008 anti-gay marriage “Proposition 8” that sparked the controversy. Mozilla, a nonprofit organization, is heavily committed to “keeping the web open” as well as to values of equality and inclusivity. In response to Eich’s promotion, a number of key employees and developer groups called for his resignation on Twitter and other social media sites. Eich responded in a personal blog post that he would continue Mozilla’s effort of “commitment to equality in everything we do.” Critics are largely unsatisfied by the response, demanding either a retraction and apology from Eich or his resignation. Complicating matters, three of Mozilla’s six board members resigned this week, citing their desire to hire an outsider with expertise in mobile computing.
Can a CEO have personal values that conflict with the values promoted by the organization and still be an effective ethical leader for the organization? (Focus on leadership qualities and factors rather than on the specific views expressed by the CEO.)
LA 2: 
Scenario:  Branford Home Goods Inc. (Branford) is considering genetic screening of its potential employees and current employees.
Branford has retained Veritas Diagnostics, a medical diagnostics company specializing in adult genetic susceptibility testing for a range of heritable and complex genetic conditions. Their main business involves testing for mutations associated with cystic fibrosis, hereditary kidney disease, as well as breast, ovarian and colorectal cancer.
Veritas has a well-staffed, well-run, sophisticated genetics laboratory capable of rapidly processing hundreds of samples for analysis on their many automated high-throughput DNA sequencers. Veritas’ testing methodology is considered the ‘gold standard’, and Veritas implements the latest testing technologies available. Further, Veritas maintains good working relations with leading university research laboratories, with whom they regularly verify their testing methods.
Veritas’ chief clientele are hospitals, physicians, and private insurers ordering genetic testing for patients. The company has become known for providing quick, accurate, and confidential services at a competitive price. Veritas has decided to expand its genetic testing services to other industries and companies.
As corporate Ethics Officer for Branford you have been asked to work with Veritas’ VP to ensure that the genetic screening services for Branford are provided in an ethical manner. As Branford’s Ethics Officer, you are concerned with the ethical issues of fairness and employee privacy. Veritas already has privacy rules for dealing with physicians, hospitals, and insurance companies, and the Veritas VP believes these procedures are a good fit for Branford with only minor adaptations.
You, however, see the situation as being more complex, and so are faced with aIDressing the following ethical questions and working with Veritas to resolve them:

Should Branford develop a formal ethics policy statement dealing specifically with issues related to the genetic screening for employees? And if so, what points should be included in the policy?
Who owns the genetic material used for testing – the employee, Branford or Veritas?
Can the material used for testing be sold or donated by Branford or Veritas for research purposes?

Adapted from “e-Health and Commercial Genetic Testing”. ©   Bryn Williams-Jones. This case is fictitious; Veritas Diagnostics does not exist. Permission is hereby given for printing & copying this case, for educational purposes, provided that the author’s name and the URL are included.