As you say, one goal of a paper is to certify that something is true. But the author should be more concerned with the result's certifiability than any reader. The author, being human, also requires the result to be broken up into smaller and more easily verified pieces. I can't count the number of times that I have proved a statement modulo certain details, and upon writing them up carefully I discovered that a new case emerged or the statement of the theorem needed to be altered in some (perhaps material) way.
The introduction of a paper is a great place to sketch an overview or give heuristics ... most readers will not venture beyond it anyway.