The implication must be that, similar to the Executive staff’s secret agreement to, at all costs, prevent the president from impulsively starting a nuclear war, the secret service detail realized they were dealing with a spoiled narcissist’s tantrum… they were prepared for it and acted prudently.
As the author points out, they had no actual authority to defy the president’s order. But, they did so anyway, because (a) they were all in agreement that it would have put POTUS in grave danger, both physically and legally, and (b) he was too stupid and helpless to do any about it in real time anyway.
Of course, the agents will deny it because it would be an admission of abrogation of duty, even though, ironically, their action was also consistent with the federal oath to protect and defend the constitution. Talk about being stuck between a rock and a hard place! Whooee!