Yes, but this has to be built into the experiment, or at least considered in the statistical analysis. You cannot just stop something when it's statistically significant.
You have to be extremely careful about this, otherwise you can end up with much worse significance than simple analysis would suggest (and then that kills people).
Yeah, "Stop when the results are positive" is one of the classic ways to fudge a study. Twelve patients (the number mentioned in the article) is way, way premature to end this early.
In this case, it's not even the regulatory environment. As the article mentions, the treatment is as fantastically expensive as it is fantastic. A lot of the skepticism isn't that it can't work, but that it might be too expensive to be viable.
You have to be extremely careful about this, otherwise you can end up with much worse significance than simple analysis would suggest (and then that kills people).