Since 2021, a security conference in Atlanta had played host to a simple tabletop exercise in which attendees talked about how they would respond to fictional disasters like plane crashes or water treatment issues.

Sitting around a big table, participants from federal agencies or local departments devoted to emergency preparedness shared how their crews would react. Round and round they went, role-playing, sometimes for hours, as the scenario got more complex.

This year’s meeting was scheduled on Nov. 5 — Election Day — with the fictional scenario expected to focus on transportation, or possibly the chemical industry.

For conspiracy theorists who have fixated on falsehoods about widespread election fraud, though, the timing alone was enough to transform the event into something far more sinister. They spread claims that the conference was a secret meeting of top federal security experts in a bid to hack or steal this year’s presidential election — though it was neither of those things.

As news about the conference spread online, conspiracy theorists painted the event as cover for a “cyberattack” on election infrastructure or a fallback plan to somehow flip Georgia to Democrats should former President Donald J. Trump lead in early voting.

The Republican National Committee and Senator Rand Paul joined in on the criticism, issuing letters asking for more details about potential involvement by federal security agencies and implying that the agencies might have been distracted by the conference during a crucial election period. A spokeswoman for Mr. Paul shared a conference agenda showing the Department of Homeland Security was expected to participate. Organizers and the D.H.S. said they had not confirmed.