—Secret service has a right to control its own security detail and impose conditions on the audience.
Only people have rights. The US Secret Service has policies.
The police chief did the right thing in leaving, but assumed incorrectly that a candidate controls secret service polices.
I agree, was just using shorthand. Much easier than "The Secret Service has the power to exclude people from exercising their right to be armed in a venue where it is protecting a candidate or official."