The Secret Service did not respond immediately to a request for comment.
The incident also raised questions about Clinton's travelling pool of reporters, which she left behind at ground zero when she departed unexpectedly, leaving the press with no knowledge of her whereabouts or condition for about 90 minutes.
Clinton travels with a small group of reporters and photographers representing broadcast and print outlets. The arrangement, called a "pool," approximates the rotating group of press outlets that travel with the president.
Trump has no such pool, a break with past candidates. He had no reporters with him today, when he appeared unannounced at the same September 11 memorial ceremony Clinton attended.
Clinton resisted very close contact with her pool over the northern summer, consenting only to travel on her own small jet in tandem with the pool and not allowing the same kind of full-time coverage customary at the White House.
Starting on Labour Day, Clinton began travelling on the same large campaign plane with her Secret Service detail and reporters, and the pool has had greater access to some of her events including a findraising party in New York on Saturday. It was at that event when Clinton stirred controversy by referring to some Trump supporters as "deplorables."
In the White House model, a so-called protective pool is on constant standby each day, until given an all-clear that the president will not have any further public events or outings. That model has been followed more closely by presidential candidates in the past.
Clinton is not allowing door-to-door pool coverage, in which the pool group would assemble at her home and travel with her from there. Instead, pool reporters have met up with Clinton at her plane or elsewhere. Today, the pool was left behind both when Clinton departed the memorial and when she departed her daughter Chelsea's apartment. The pool was later driven separately to Westchester County, where Clinton lives.
Robert Gibbs, President Barack Obama's first White House press secretary, suggested in a tweet today that it's time for Clinton to adopt a more formal protective pool.
"Protective pool isn't always easy for either candidate or press but there comes a point for each nominee when it must be part of daily life," he said.