A problem with this experiment is that while Bill may be the same person in Interview A and B, the interviewers are not the same person. You can't know for sure if the VP in A would act like the CEO in B if Bill was interviewing for a managerial position. It is just as likely that the VP in A is simply a jerk who tries and one-up all interviewees, regardless of the status of the position they are interviewing for.
Here is an interesting blog post about a guy who did a resume experiment between two positions which he argues are by experience identical, but occupy different "social status" positions in tech: A software engineer and a data manager.
The author concludes that positions that are labeled as code-monkey-like are low status, while positions that are labeled as managerial are high status. Even if they are "essentially" doing the same sort of work.
Not sure about this methodology, but it's food for thought.