Athenahealth has been treading water for years, last spring attracting the generally unwelcome attention of Elliott Management, the world’s largest and most aggressive activist investor, which bought a 9.2% stake. (See Jen Wieczner’s feature on Elliott from the Dec. 15, 2107 issue of Fortune.) The stock has stagnated in part because Athenahealth has developed a bad habit of overpromising its next product’s wonders; customers and investors, while mostly praising the company’s strategy—“It’s just what our industry needs,” says a major customer—discount the future deeply. In their world, Immelt represents the good side of established, sober corporate America, a counterweight to Athenahealth’s undisciplined happy talk.

It’s ironic that within GE, Immelt was often accused of overpromising. “The marketer,” he was sometimes called, a reference to his early assignments. “There’s no question that he overpromised,” says a former GE colleague. But that’s a detail that doesn’t bother most outsiders. (Through a spokesman, Immelt declined to comment.)

In addition, he can call pretty much anyone on the planet. That’s why an RBC Capital Markets analyst called him “a door opener and deal closer” for Athenahealth. And he knows the business, having run GE’s healthcare operation before becoming CEO and then building that business further, in part by buying healthcare IT assets. For Athenahealth, he’s a catch.

For Immelt, talk of redemption via this new role is way overblown. His 16-year tenure at GE is an ugly story, made worse by its disastrous ending. Soon after he stepped down as CEO on August 1, successor John Flannery announced that things were much worse than previously disclosed. The stock, already in decline, plunged 45% last year while the S&P rocketed 18%. GE was the Dow’s worst performer in 2017, as it was over Immelt’s entire tenure. Redemption from that record will take much more than becoming non-executive chairman of a small software firm. It may be impossible.

So what is Immelt getting? As he turns 62, he isn’t ready to leave the stage. He allowed Uber’s board to consider him as a possible CEO last year before taking himself out of the running, and he recently joined Silicon Valley’s New Enterprise Associates venture capital firm. He’s teaching a course at Stanford business school called “Systems Leadership for the Digital Industrial Transformation.” Now Athenahealth offers a low-key re-entry into the world of publicly traded companies and changes the subject from GE, further positioning him as a player in the world of tech startups. It doesn’t hurt that Athenahealth is headquartered near his new home in Boston.

But every pairing carries risks. The main risk for Immelt is that Athenahealth goes nowhere, furthering the Immelt’s-a-bust narrative; Wall Street analysts are sharply divided on the company’s future. That risk looks small if only because Elliott Management usually makes money on its investments. It presumably approved Immelt’s appointment. (Elliott did not respond to Fortune’s request for comment, and Athenahealth said only that “we don’t comment on specifics” of conversations with shareholders.)

Athenahealth’s risk is that Immelt’s GE problems may not be behind him. The Wall Street Journal revealed last fall, after Immelt was gone, that for years GE flew an empty corporate jet behind his plane when he traveled to hazardous locales. He claimed he knew nothing of that policy until 2014 and stopped it. But the Journal then reported that the practice continued at least until last March. (GE declined Fortune’s request for comment.) “What is Athenahealth thinking?” wonders Charles Elson, director of the University of Delaware’s John L. Weinberg Center for Corporate Governance. “When you put someone in that position [of chairman], you don’t want that person to become a lightning rod for criticism. He could affect how the company is perceived.”

Potentially more worrisome is a new SEC inquiry into accounting and revenue recognition at GE during Immelt’s tenure. In January GE blindsided investors by announcing a $6.2-billion charge to earnings based on accounting practices going back years. The inquiry’s outcome can’t yet be discerned, and GE says it is “cooperating fully.” But the inquiry could lead to a long-running trickle of bad news with Immelt’s name attached.

Jeff Immelt and Athenahealth—what do those two see in each other? It’s an old story. Both have something to lose but also something to gain. Probably both wish they were in a position to be choosier.