That’s a hard sell for many voters. (To belabor the metaphor: Where, then, is the smoke coming from? A smoke machine?) For now, there is no visible conflagration. The Clinton family has never taken a salary from the foundation. The watchdog group Charity Watch awarded the foundation an A rating for its financial management. It’s hard to quarrel with the legitimate good works the foundation has done in the developing world.

But the foundation’s good works are a separate issue from donors’ links to Mrs. Clinton in her role representing the public. The rules that apply to private citizens are much different from the rules (written or unwritten) that we apply to presidential candidates. And sometimes, the simple suggestion of corruption can be as damaging as real corruption to a candidate’s reputation.

Earlier this month, the foundation announced that if Mrs. Clinton was elected, it would stop accepting money from foreign and corporate donors. The foundation would also spin off some of its programs to partner organizations — though which organizations remains unclear. And Mr. Clinton would step down from the foundation’s board, while Chelsea Clinton would remain on the board.

Lawrence M. Noble, the general counsel at the nonpartisan Campaign Legal Center, said the Clintons had been “somewhat tone deaf” about how their relationship with donors would be perceived. Still, he said the focus on Mrs. Clinton’s meetings as secretary of state is a “distraction” from the real problems with our campaign finance system — a system that the Clintons and other politicians benefit handsomely from.

“The problem is that we’ve developed this culture in part thanks to the Supreme Court that seems to sanction the idea that donors will get special access,” he said. “As long as we see this potential influence, we’re not going to trust it, because it’s human nature that one is influenced by those who are trying to help them.”

It’s impossible to know what inspires a donor, in his heart of hearts, to give a large sum of money to an organization. But critics like The Intercept’s Glenn Greenwald have argued that some donors such as Saudi Arabia and Qatar — which have abysmal human rights records toward women and gay citizens — may have less-than-ideal intentions.