1. Reports like this raise questions regarding the status of non-Christian or occult exorcism:
This issue crops up, not only in reference to Catholic exorcists, but also cult members and witchdoctors. (By non-Christian, I'm not necessarily including Jewish exorcists. God might well honor exorcisms performed by Jews in OT and Second Temple Judaism.)
2. I assume the standard Christian objection to the possibility of non-Christian/occult exorcism is this:
25 Every kingdom divided against itself is laid waste, and no city or house divided against itself will stand. 26 If Satan casts out Satan, he is divided against himself; how then will his kingdom stand? 27 If I cast out demons by Beelzebul, by whom do your own exorcists cast them out? Therefore they will be your judges. 28 But if it is by the Spirit of God that I cast out demons, then the kingdom of God has come to you. 29 Or how can one enter a strong man’s house and plunder his property, without first tying up the strong man? Then indeed the house can be plundered (Mt 12:25-29).
3. Although I haven't done a survey, I presume many readers think what he says precludes occult exorcism. If their interpretation is correct, then we must summarily discount all reported cases of occult exorcism, however well-documented.
4. Consider a different interpretation: Christ is using a tu quoque argument. Posing a dilemma for his accusers. Whichever way they answer they will lose the argument. Reinforcing this interpretation is the fact that v27 takes the explicit form of a tu quoque argument. On that interpretation, Jesus isn't ruling out occult exorcism, but responding to his accusers on their own grounds and putting them on the defensive–without endorsing the assumptions of the argument. A tu quoque argument is a kind of ad hominem argument or argument from analogy–where the speaker temporarily adopts the opposing viewpoint for the sake of argument.
5. Assuming that leaves open the possibility of (successful) occult exorcism, what might be the motivation? One can imagine the dark side using occult exorcism as a tactic to delude the masses into following a false religion. The demon cooperates with the exorcist because that lends credibility to the false religion. So that wouldn't be a case of the dark side working at cross purposes. Rather, it collaborates with human representatives of a false religion to lead people astray.
6. Here's another possible motivation. I guessing that many Christians think the dark side has a militaristic command structure with Satan at the top. Demons take orders from Satan and his lieutenants. The dark side is a unified "army of darkness".
Perhaps, though, the dark side is more like rival crime families. The fact that they all hate God doesn't mean they like each other. Indeed, given the psychology of evil, demons may well detest each other. They hate everything. Maybe the dark side is riven with turf wars and competing power centers.
Or it might be like a military dictatorship where betrayal is the mechanism of promotion. Subordinates collude to frag their commanding officers and take their place. On both comparisons, the dark side is both united and disunited. United in common opposition to God and the good, but disunited insofar as they jockey for dominance among each other.
7. Apropos (6), maybe some demons are more powerful than others. Maybe some angels are more powerful than others, by divine creation, and when they fall they retain the power disparity. If so, perhaps the most powerful demons are bullies who like to push around weaker demons. In that respect, a stronger demon might overpower a weaker demon and expel him from a demoniac just to throw his weight around.
This is all speculation, but it's consistent with the phenomenon of occult exorcism. It proposes different backstories to explain the phenomenon. Although they go beyond revelation, they have a starting-point in revelation. A possible inference.
8. What Christ says has specific reference to the demonic realm, but it may be the case that humans can be possessed by the souls of the damned as well as demons. If so, that falls outside the immediate purview of Christ's statement.
9. Another issue is whether there are follow-up studies on occult exorcism. Is it permanent? Witchcraft can be effective, but there's a catch. It replaces one thing with something worse. Occult healing or exorcism is a curse in disguise.
10. A possible objection to the alternate interpretation (4) is that if Christ's riposte is merely a tu quoque argument, then he failed to directly refute the allegation. So where does that leave the allegation?
Assuming the alternate explanation is true, perhaps he resorted to a tu quoque argument because a direct refutation would be too complex to articulate in that setting. But if his answer leaves the allegation hanging out there, is there a way to refute it?
i) From a tactical or strategic standpoint, one can understand how the dark side might play along with exorcism if that promotes an evil religion, steering people away from God and redirecting them into the hands of Satan. If, however, the Christian faith has the opposite effect, then the Jewish allegation is counterproductive. The Christian faith is liberating people from depravity and occult bondage.
ii) That allows us to differentiate purer forms of Christianity (e.g. evangelicalism) from more adulterated forms (e.g. Catholicism) or cults (e.g. Mormonism) or paganism (e.g. witchdoctors). So the success of exorcism in divergent religious contexts has different, but consistent explanations.
iii) In addition, Christianity has a special relationship to Judaism that's lacking in paganism or even Islam. If Christianity is false, then God has allowed a false religion to completely obscure the true alternative (rabbinic Judaism), as the perceived successor to Judaism. In that case, rabbinic Judaism is like a candle at high noon. You can barely see it because the overwhelming brightness of the alternative all but drowns it out. Moreover, Muhammad wasn't an exorcist or wonder-worker, so there's no comparison at that level.