During the 2yrs in IIM, many courses were analytics based like those on statistics, managerial computing, system flowcharting etc. The 'softer' HR subjects were scoffed upon by me and many batchmates as 'globe', atleast in the academics and assessment. While many profs/seniors used to stress the importance of HR courses, I felt that those skills would be learnt on the job unlike hard skills in which prior knowledge may help in serendipity and saving sleepless nights. Also, given the cooperative/common goals in MBA versus that in the workplace(often dog-eat-dog), it is doubtful
When you are new to the organization, taking process walkthoughs/interviews/mystery audits will only help till a point, and will probably tell you how things are supposed to work-process walkthoughs will show the inside view of the process, while Hawthorne effect ensures that getting a realistic view is difficult. Data is never biased(atleast should not be), so as long as you can conduct exploratory data analysis using pivots, filters, lookups etc to get a broad picture. And it is analysis which is necessary to show that you are just not spouting MBA jargon as the new whizkid on the block, but have actually understood the process and all.
Often, there will be things which you feel is 'broken','flawed','wrong' etc. But to counter the 'why fix it if its not broke', you need data to back you up. When data is not available, then seniority in the room wins but otherwise only data can counter data. Of course, do not get into the trap of analysis paralysis-conclude your analysis at a cutoff point, then followup persistently to implement your findings.