Your coach is absolutely correct! These questions are NOT clarifying questions! These are questions which already perform specific analyses.
The purpose of the clarifying questions is to enable you to create a structure. A structure is the LOGIC according to which the analysis will be conducted and which will invariably lead to the answer of the question.
None of these two questions has ANY impact on this logic! At the start of a case, it is completely useless to ask for whether it is industry-wide or company specific, since you will have to find out the mathematical cause of the issue anyway. In other words - the answer to you question is irrelevant for the pricipal analysis logic. It will not change ANYTHING in your structure.
So what you need to understand are things like objective/focus metric, business model (so you can properly create a driver tree below the focus metric), secondary concerns of the client (if any). THIS is what you must understand to create a robust logic.
The two questions you outlined are typical for the weak advice you receive in many resources. They are only helpful if you don't know how to perform rigorous analysis. If you just guess around and think in buckets. Then these two questions might help you define where to start with your guessing. But this is not the kind of methodical thinking that will lead to a high success chance in MBB interviews.