I appreciate you sharing the article; in my opinion, it provides a solid synthesis of the majority of the relevant information. However, I believe it skirts the main point of the original poster’s query and the overall discussion of “sense” (as an intuition) versus “sense” (as the application of judgment and decision-making in the real world).
It also surprises me that, at least as of this writing, no one else has directly addressed the “intuition” sense in a remark. So I’ll try it (based only on the opinion of one random internet user, of course):
Product Intuition (what interviewers mean): The ability to have and demonstrate a ‘product centric’ mindset and intuition around what makes products great and improves them - independent of the particular product domain
Ex. Someone who has a strong product intuition, would be able to abstractly and naturally describe what makes for a ‘good’ product.
More precisely though and in practice, it means having an ‘intuition’ not just around decisions, but also when you do not have enough information to be confident. It means knowing when you don’t know, and when information is limited but decisions need to be made, being able to apply that level of confidence as a part of how things are implemented.
In many ways though, product intuition is about mindset, perspective and ‘feel’. Its the difference between jumping to ‘product frameworks’ directly for ‘the right answer’ rather than intuiting the relevance of each framework, and applying parts of it as is most effective. (studying frameworks ≠ having product sense)
Product Judgement (specific product and domain advocacy): This is what I believe is what the commenter and the article you shared is referring to - the how to make better products in a way that is independent from one’s sense - but is strictly viewed in the lens of the specific customer problem, pain point and what they are actually paying you for.
I think true product judgement can only be properly curated over time as a function of experience and exposure in a specific area. (You must understand your operating landscape)
Ability to develop and build one’s product judgement is a requirement to be anything more than a half-decent PM. Excellent PMs have a well built product judgement.
Combining these independent factors together: IMO, ‘product judgement’ when combined with powerful ‘product intuition’ is the mega-combo, and is what makes incredible PMs, incredible.
Half expecting to be down voted for this view - but these are definitely different dimensions of the same conversation, and seem to be intermingled when discussed. I do believe Product Intuition can also be developed, but it also requires a very open and curious ‘learning mindset’.