It is difficult to give a "global" answer to this question.
There is a very wide variety of PhD programs in statistics throughout the world, so much so that the overlap between two given programs can end up being surprisingly small.
The closest thing to a short answer is: Yes, it helps. (Or, should!)
Now, for some nuances.
Any scholarly peer-reviewed publication should be viewed favorably. Obviously, the closer your publications are to the field that you're applying to, the more weight they are likely to receive. People – even academics – tend to go with what they know and are familiar with. If the journal/conference is recognizable to them, then that will help, but it's not a prerequisite.
If, for example, you apply to any top-tier PhD programs in statistics, you'll mostly be competing against other applicants with undergraduate degrees in mathematics, so a publication in a reputable journal/conference can help set you apart.
Personally, I disagree with your second professor: I'd be very happy to see a publication in history or literature (or whatever) if accompanied by an otherwise strong application. But, I may also be in the minority there.
It depends on the departments you apply to. Many statistics departments in the US, e.g., have become increasingly attuned to the overlap in statistics, machine learning, and computer science, in general, over the last many years. Some have very active research groups in this area and regularly interact (and collaborate) with machine-learning researchers from other departments and publish in NIPS, ICML, JMLR and other like venues. And, some departments simply have more active research programs, generally speaking, than others.
Applying to departments that have focused research programs in statistical machine learning will improve the chance that your publication will be given greater weight, especially if it is published in a high-profile venue. Other departments that are either more traditional or have different research foci may weigh such a publication differently. In any event, you should try to be aware of how well aligned your interests are to those of the departments you're applying to, assuming your interests are at all well-defined at this stage.
Talk about your research. If your application includes a personal research statement of some sort, discuss your work and describe the statistical content in a concise, matter-of-fact way. If it genuinely led to your interest in applying to PhD programs in statistics, then you can describe this as well, but it should be natural and not forced.