For Bill Clinton, the rarefied world of private plane tarmacs has long been a place for a former president to socialize. Last month, after he spoke at the funeral of Muhammad Ali in Louisville, Ky., Mr. Clinton ran into Senator Orrin G. Hatch, Republican of Utah, and the two chatted before their private jets took off.

Then there were the times Mr. Clinton spotted Representative Paul D. Ryan, the House speaker, and Arnold Schwarzenegger, the former Republican governor of California, and gave them each warm greetings.

A Clinton aide pointed to Mr. Clinton chatting with Senator Ted Cruz, who has called for Hillary Clinton’s imprisonment, at the airport in Mobile, Ala., as evidence that the 42nd president would say hello to anyone he sees on a tarmac.

But on Monday, the practice brought a world of political problems for Mrs. Clinton.

Mr. Clinton had just finished a stop on a seven-state, 10-event fund-raising swing for his wife’s campaign when he was boarding a private charter at the Phoenix Sky Harbor International Airport. (The visit did not include playing golf, despite reports to the contrary.)