Wells Fargo CEO John Stumpf looked like a man adrift on Tuesday.

Over the years, both the 63-year-old son of a farmer and the massive bank he heads have nurtured a reputation as respectable, gentle and neighborhood-focused, in contrast to the cutthroat Wall Street world of their peers. Then, just over a week ago, bombshell news broke: The bank was being fined $185 million after thousands of Wells Fargo employees defrauded customers by opening millions of accounts without permission, losing Americans a collective $2.5 million in illegitimate fees.

Which brings us to Tuesday, when a contrite Stumpf showed up before the Senate Banking Committee to account for what happened. "I accept full responsibility for all unethical sales practices in our retail banking business," he stated in his prepared testimony. But as the hearing wore on, Democrats and Republicans alike became increasingly frustrated with Stumpf's answers, culminating in a seven-and-a-half minute torching by an incensed Sen. Elizabeth Warren (D-Mass.).

The hearing revealed an almost-existential problem for Stumpf: Namely, what exactly does he do all day?

Obviously, in a literal sense, he's Wells Fargo's chief executive officer, tapped by the shareholders to lead the company, with all the managerial powers and duties implied therein. But this position also implies a certain narrative: that the "buck stops here," as Sen. Richard Shelby (R-Ala.) put it; that the captain, being responsible for the course of the ship, goes down with it.

But Stumpf's question and answer session with the senators revealed a CEO who seemed to have no idea what his bank was doing or to have much power over it.

Reports by the Los Angeles Times and the L.A. city attorney have made it clear that there has long been a culture of fear, born of threats to workers' livelihoods and impossible sales goals, at Wells Fargo. And a recent Wall Street Journal timeline reported that bank executives were getting hints of rampant bad behavior as early as 2009, and that the bank had a unit investigating the problem by 2012. The 5,300 employees fired for the fraud were terminated between 2011 and 2015, with the peak of the culling in 2013.

Multiple employees have complained of a company culture that encouraged fraud by setting impossible goals in "crossing-selling" — ie. selling multiple accounts to the same customer — and then offering big bonuses to employees who hit them. Tuesday's hearing clarified that Wells Fargo's sales goal was eight accounts per customer, while most banks average only three.

Yet Stumpf recently insisted in a Wall Street Journal interview that "there was no incentive to do bad things." To CNBC's Jim Cramer, he claimed "there is nothing in our culture, nothing in our vision and values that would support [that behavior.]"

In front of the Senate Banking Committee, Stumpf seemed to have difficulty grasping how a low-level bank employee with a family could feel financially cornered while making $35,000 to $60,000 a year. (As Sen. Sherrod Brown (D-Ohio) pointed out, Stumpf makes about $19 million a year.) As earnest and gently-spoken as Stumpf was, the senators seemed to unanimously conclude that he was throwing his workers under the bus. "To us at least you minimize your influence" Brown concluded.

Then there's the matter of Carrie Tolstedt, the senior vice president for community banking, who was in charge of the 6,000 or so branches where the fraud occurred. She retired with little fanfare this July, complete with a $125 million payout, despite the fact that the sales practices of her corner of the business had been under the microscope for over a year. Many senators were incensed over this detail in particular, asking if Stumpf would recommend that Wells Fargo make use of clawback provisions to retrieve that pay. The CEO insisted that, despite being CEO, the matter was out of his hands, that it would be determined by the appropriate body within the company, and that he would only bias the process. Even when asked if he would return his own pay, Stumpf replied it was up to the company board.

But the most brutal moments arrived when Warren took her turn, ripping into Stumpf's "gutless leadership." After clarifying that no senior executive at Wells Fargo has been fired, and that Stumpf won't be returning his own pay or resigning, Warren dropped a stack of 12 quarterly earnings calls Stumpf himself made with investors from 2012 to 2014. In one annual report, Stumpf defended Wells Fargo's eye-popping sales goal of eight accounts per customer by declaring, "it rhymed with 'great,'" and that "Perhaps our new cheer should be: 'Let's go again, for 10!'"

"In all 12 of these calls you personally cited Wells Fargo's success at cross-selling" as one of the main reasons they should invest, Warren said. In fact, Wells Fargo passed JPMorgan in 2013 to become the bank with the highest stock market capitalization, and didn't fall behind again until last week. Warren noted that Stumpf himself owned millions of shares, and that the bank's stock market gains alone netted him $200 million. "You squeezed your employees to the breaking point so they would cheat customers and you could drive up your stock," Warren concluded, insisting Stumpf should resign, give back his pay, and face a criminal investigation.

And the thing is, even if Warren is wrong and Stumpf wasn't cognizant of wrongdoing, he doesn't come off looking much better. Either Stumpf was maliciously, self-servingly irresponsible, or he was completely oblivious. In either case, there's a pretty obvious implication that you can't just say you accept responsibility; you have to demonstrate it. And so far, no such demonstration has been forthcoming from Stumpf.

The $185 million fine Wells Fargo will pay is a pittance — 3 percent of its second quarter profits. No senior executives have been fired, nor does it seem they will be. Wells Fargo announced it will eliminate the sales goals from its retail banking business, and put better processes in place to make sure customers know and consent when accounts are opened in their name. But the cross-selling will continue.

"I think the best thing I could do right now is lead this company forward," Stumpf told Cramer.