Eleven years ago, one of Washington’s most tradition-bound companies placed a bet that would transform its fortunes. The wager, by The Washington Post Co. and its Kaplan division, took the form of a $165 million purchase of an Atlanta-based chain of for-profit vocational schools that catered to low-income students. The bet was big — the price equal to the profits earned that year by The Post Co.’s print-media pillars: this newspaper and Newsweek magazine. So was the payoff. But what proved a deftly timed business move brought other, less welcome scrutiny to a family-run company that had long prided itself in serving the public interest.