Sociopaths would presumably struggle to pass a V-K test, as might someone who is on the autistic spectrum.
As somebody on the spectrum (ADD, Asp), I very much disagree.
It's an old and very harmful trope, thoroughly discredited by now. Neurodivergent people do not lack empathy, if anything we have an overabundance of it, from all the social strife and hardship ensuing from the complications in our social interactions. Aspies fail to read intent or subtext, some of us fail to read when and which emotions happen in a person, based on their social cues and body language - this absolutely doesn't mean we do not understand or feel the emotions themselves. We fail to convey the socially appropriate amount of emotion (we think we've calibrated our communication well, but we "send" messages that read as too much or too little), but we rarely have an issue with empathizing with others' emotions.
As Aspie, I might have trouble recognizing that because of what I said, a "face value" reply to someone, that person feels rejected and undervalued now. If I knew (e.g. that person or a third person tells me "hey, what you just said wasn't what they expected, the wanted acceptance and reinforcement of their self-worth, now they're dejected and depressed because of what you said"), I would be horrified because that was not the intent. A sociopath would not care. They would not have empathized with that person's suffering.
A V-K test is encapsulated within the turtle question. "A turle is lying on it's back. (It's suffering.) You do not help." - an autistic person would be horrified, "why wouldn't I help?! let me help!", a sociopath would think "why would or should I help? do I gain anything from it? is this how I pass the test?". A true sociopath only mimics empathy and that's the game they play in V-K, until he's found out.