As jurors in lower Manhattan this week debate Mathew Martoma’s guilt on insider-trading charges, the trial, which heard closing arguments on Monday, has raised another question: How was Mr. Martoma—after being expelled from Harvard Law School for forging a transcript—accepted by Stanford Business School and then hired by a prominent hedge fund?

Mr. Martoma changed his grades to As and submitted the false transcript in his application for a clerkship with a federal judge in 1999. After Harvard discovered the offense and expelled him, the former Ajai Mathew Thomas changed his name to Mathew Martoma. As this story spilled out in the lead-up to his criminal trial, many began asking whether Stanford and his former employer, SAC Capital Advisors, bothered to look at Mr. Martoma’s history. And if background checks were performed, why did they miss these red flags?

The Martoma “conundrum,” as it has been dubbed in the media, reflects a frustrating paradox in the growing due-diligence industry. With advances in Internet search technology and a proliferation of investigative firms, why do we continue to see high-profile cases in which an employee’s prior transgression or act of concealment embarrasses a well-known company or university?

In recent years, executives at Yahoo, Veritas Software and the U.S. Department of Homeland Security, as well as a number of university administrators and coaches, have been fired or pressured to resign for misrepresenting their credentials. Last July, for example, Leslie Cohen Berlowitz, the longtime president of the prestigious American Academy of Arts and Sciences, was forced to resign for falsely claiming on federal grant applications that she held a doctorate from New York University.

Surely a prospective employer would have wanted to know that Mr. Martoma previously created a forged document that deceived prospective employers, including federal judges, and then created a fake email and computer forensic company in the attempted coverup.

Unfortunately, there are many reasons why exclusive institutions end up hiring employees with misleading credentials. In some cases, top companies and universities hire individuals without conducting any background inquiry. In other cases, the background check fails to uncover information that should have been found through due diligence.

Some companies choose not to conduct due diligence because of the common false assumption that a prior employer must have run a background check that produced no negative results. That choice can lead to a situation in which an unethical executive rises to the top without ever being properly screened.

Often a single background check isn’t adequate or reliable. Take Washington Navy Yard shooter Aaron Alexis, the 34-year-old former Navy reservist and computer contractor who killed 12 people on Sept. 16, 2013, before being shot and killed by police. In 2004, Alexis was arrested for malicious mischief for shooting out the tires of a car but was nonetheless granted security clearance in 2008. In 2010, he was again arrested for a gun-related offense but did not lose his security clearance.

This sort of lax oversight of employees is not uncommon. While some employers follow thorough processes before hiring an employee, many do not conduct subsequent background reviews after the individual is hired.

Moreover, less-sophisticated investigative firms often conduct low-budget, glorified Google searches, which may not catch a name change or other nuances. Many government and industry databases and sources cannot be effectively searched with Web search engines. To adequately scrutinize a target’s history, investigators must be aware of and have access to specialized databases, many of which are obscure or expensive to access. Some valuable sources of information, such as court records in certain jurisdictions or county regulatory actions, are still not available online, requiring an in-person visit to the courthouse or agency.

Even investigative firms with adequate resources may miss clues and leads that can provide valuable “second level” information. Some run searches and simply provide the client with a memorandum that mirrors the database results. That is the equivalent of a physician handing you the raw data from your blood labs and EKG.

The risks and limitations of due diligence grow when the hiring employer needs information overseas. An unsophisticated investigator may not grasp the sensitivity of data privacy laws in other countries and how they differ even among neighboring nations. Employees today often have footprints and history in multiple countries, and employers who limit their due-diligence searches to domestic jurisdictions may be setting themselves up for an embarrassing headline down the road.

Advances in technology have given employers false confidence. Anyone can pay to have their history on Google “scrubbed.” In Mr. Martoma’s case, it is unlikely that SAC would have uncovered his name change—and subsequently his misconduct at Harvard—by simply searching online. Yet with a more thorough due-diligence search, Mr. Martoma may not have ended up at the hedge fund—and the firm would have had one less headache.

Mr. Lenzner, a former federal and Manhattan prosecutor, is the executive vice president of Investigative Group International Inc.