Penny Pritzker, one of America’s richest and most powerful businesswomen, is no longer considered an independent director of Hyatt Hotels Corp., the publicly traded company that her family controls.

Hyatt disclosed that change in its proxy statement in late April, when the list of independent directors no longer included the 51-year-old Pritzker, who was national finance chair for Barack Obama’s presidential campaign and leads several companies that are part of her family’s business empire.

When Hyatt made its initial public offering last fall, the company designated Pritzker as one of eight “independent” directors on its 12-person board. That designation was noted in a Wall Street Journal article, which included statements from two corporate governance specialists questioning the designation, given her family’s role at the company.

Pritzker’s directorship status changed because she took over within the past year as president of a family enterprise that leases the office space to Hyatt for its corporate headquarters in Chicago, said a spokeswoman for her. In its proxy statement, Hyatt said the company paid $10.4 million in 2009 under that lease.

When Pritzker was designated an independent director last fall, various family businesses where she was chairman or president did about $3 million a year in transactions with Hyatt.

Pritzker’s new duties apparently made her dealings with Hyatt “material” enough to disqualify her as independent.

Some corporate governance experts also question the independence designation still given to two other directors who have outside business ties to the Hyatt or the Pritzker family, though these observers don’t accuse the company of violating applicable standards. “Those relationships clearly raise independence issues,” said Charles Elson, director of the Weinberg Center for Corporate Governance at the University of Delaware.

Without those two designations, Hyatt’s board wouldn’t have the majority of independent directors normally required by the New York Stock Exchange, where the company’s shares trade. Under the exchange’s definition, an independent director can’t have too close a family relationship with a top company official or a material outside business relationship with the firm.

A Hyatt spokesman declined to comment. The company said in Securities and Exchange Commission filings that its directors meet applicable independence standards and are able to make decisions free of conflicts. Of the current 12 directors, seven are designated as independent.

The question of the independence of Hyatt’s board fits into a debate that’s been going on for over a century. In the years after the Civil War, courts took a dim view of so-called related-party transactions, where directors had separate business dealings with the company. However, as modern corporations rose in the 20th century, related-party transactions became more tolerated, say business historians.

The NYSE first established director independence requirements in the 1950s.

The last big expansion of listing standards related to independence came in 2003 following a wave of corporate scandals led by Enron Corp. At Enron, the the board tolerated massive related-party transactions by the chief financial officer that eventually helped sink the company.

On director independence, “there has been improvement” during the past decade, said Patrick McGurn, special counsel at ISS, a shareholder advisory service.

Current NYSE standards bar close relatives of a senior executive from being deemed independent. But that definition doesn’t cover first cousins, which is the family tie Pritzker has to Hyatt’s executive chairman, Thomas Pritzker.

Much of the independence debate revolves around what qualifies as a “material” business relationship.

Hyatt determined that Byron Trott, managing partner of BDT Capital Partners LLC is independent even though a firm where he is president serves as an adviser “on a broad range of matters” to Pritzker family trusts, where one of the trustees is Pritzker, according to Hyatt’s proxy statement. Plus, Pritzker trusts are limited partners in a BDT investment fund, the proxy said.

Beverly Behan, a corporate board consultant in New York, said it’s typical to have financial advisers for family trusts on the board of family-controlled companies. But usually those people aren’t considered “independent,” she said.

In Trott’s case, “it’s hard for me to imagine why there wouldn’t be some kind of conflict. It seems to me he’s there to protect the interests of the trust, which is critical to the family,” said Roger Kenny a consultant with CT Partners Board Consultants.

Trott declined to comment.

Another director designated independent is Richard Friedman, a partner and managing director at Goldman Sachs Group Inc. which served as lead underwriter on Hyatt’s initial public stock offering last year.

In 2009, Hyatt paid Goldman $3.5 million for investment banking and advisory services, according to the company’s proxy.

Friedman declined to comment.

John Arabia, an analyst at Green Street Advisors Inc., said Friedman’s designation is “misguided” and one of the reasons he lists Hyatt as having the “worst” corporate governance structure among the 30 hotel companies his firm follows.

The amount Hyatt paid last year to Goldman is only a tiny percentage of the investment banking giant’s $45.2 billion in 2009 revenue.

However, what might be a small amount of money to a big firm could still be part of a very important corporate relationship for the firm partner who serves on the company’s board, said Beth Young, senior research associate at the Corporate Library, a corporate governance research firm. The materiality standard in such situations, she said, “really misses how things work.”

Goldman had no comment on its relationship with Hyatt.