Knowing that the "lady" exhibited a particular type of "tumor" surely didn't hurt. If nothing else they had the advantage of knowing the type of tumor and x-ray pathology that was involved. This gave them ample time to study anything and everything about the condition.
The incident certainly casts a shadow on your comment on how "smart" they were. Ignoring for the moment the fact they got caught, one cannot help but wonder if their academic achievements were not a result of their "technical ingenuity".