All of the arguments I've heard against using this method assume that you have adequate supplies for alternate rewarming methods. If you literally didn't, and it appeared they were going to freeze to death anyway, would you have a whole lot to lose? Of course, if you felt yourself starting to get hypothermic as well, then I'd guess you should stop and reassess the situation, but should you at least try this method first?
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First, this answer is not a substitute for proper training. I recommend taking a class in Wilderness First Aid or higher to be better prepared for things like treating hypothermic people.
Second, hypothermia is a term that tends to have different connotations with different people. Sometimes what people call "hypothermia" is just a very cold individual, or they mean someone who is shivering uncontrollably for example. The stages of hypothermia are really a sliding scale with the varying degrees of severity sort of fading into each other. But regardless, treatment for 1st stage hypothermia is very different from severe hypothermia at the other end, especially in a backcountry scenario with limited or no resources.
For this question, a moderately severe hypothermic person seems to be the patient being referenced. Typical signs & symptoms would likely include:
With this particular patient example, warming them in the field is not a realistic prospect. You need to seek help for them, and get them out of there ASAP. Body-to-body warming, if anything, is only going to help stabilize them and keep them from getting even colder. But even then it's not a very effective way to try to warm someone in a hypothermic state, especially one of any significant degree.
But in short, body-to-body contact could be used to treat this patient as a last resort, but only as a last-ditch effort to help stabilize them until help arrives, assuming help is on the way to your location and also assuming you have no other heat sources (fire, stove...). If no help is available then trying this treatment is probably better than nothing at all. Just be careful and don't make yourself in to a patient as well!
Side note: Don't let the person get this bad! Any treatment methods including the one being discussed here (which is not the standard of care) are going to be more effective the earlier you catch the hypothermia. Time is not your friend here, so act quickly.
This article from NOLS provides some relevant information to this treatment method:
Sources: Wilderness First Aid from NOLS WMI, other training, and years of experience.
The article referenced above from NOLS.