This was addressed in the source story, Do Androids Dream of Electric Sheep?
Simply put, a human with so little social empathy as to be able to get a false-positive on the test wouldn't have been able to function in society. They would have already been immediately institutionalised.
In theory you could get a false-positive out of someone who was schizophrenic or psychopathic, but that person would have already been detectable as human by other means.
“One day, a few weeks ago, I talked with Dave about exactly that. He had been thinking along the same lines. I had a memo from the Soviet police, W.P.O. itself, circulated throughout Earth plus the colonies. A group of psychiatrists in Leningrad have approached W.P.O. with the following proposition. They want the latest and most accurate personality profile analytical tools used in determining the presence of an android—in other words, the Voigt-Kampff scale—applied to a carefully selected group of schizoid and schizophrenic human patients. Those, specifically, which reveal what’s called a ‘flattening of affect.’ You’ve heard of that.”
Rick said, “That’s specifically what the scale measures.”
“Then you understand what they’re worried about.”
“This problem has always existed. Since we first encountered androids posing as humans. The consensus of police opinion is known to you in Lurie Kampff’s article, written eight years ago. Role-taking Blockage in the Undeteriorated Schizophrenic. Kampff compared the diminished empathic faculty found in human mental patients and a superficially similar but basically—”
“The Leningrad psychiatrists,” Bryant broke in brusquely, “think that a small class of human beings could not pass the Voigt-Kampff scale. If you tested them in line with police work, you’d assess them as humanoid robots. You’d be wrong, but by then they’d be dead.” He was silent, now, waiting for Rick’s answer.
“But these individuals,” Rick said, “would all be—”
“They’d be in institutions,” Bryant agreed. “They couldn’t conceivably function in the outside world; they certainly couldn’t go undetected as advanced psychotics—unless of course their breakdown had come recently and suddenly and no one had gotten around to noticing. But this could happen.”
Do Androids Dream of Electric Sheep? - Chapter 4
Note that a functioning sociopath or psychopath (one with sufficient empathy to get along in society) would still show up as human.