Which one came first, the “meet the deadline approach” or, the “quality delivery”?

Is it really an academic thing to have to take some extra time and deliver something that shows quality rather than something that meets the client’s deadline? I heard [the wise words] of the head of my department “clients forget late deliveries, but they never forget bad deliveries”, and I felt it was right, because it fit into my view of what seems appropriate within the corporative world. But for a project manager, that is just an “academic approach”, which is not acceptable behavior in the business world [I undertand their point of view, their job is after all, to manage resources to deliver stuff on time]. Nevertheless, I felt a military approach to things, and I couldn’t avoid asking myself: Are we trying to create an environment similar to the not-so-long-gone industrial age in which our work is to produce like machines, rather than in a more hybrid, informal and conversational environment that nurtures ideas and drives innovation?

I’m totally conscious that both approaches need to meet in a middle point where deadlines are as important as good and innovative deliveries, but non should be –in my opinion- more important than the other. And there is where I stand.

P.s: I had to deliver stuff on time, and I've got to admit, it was not a bad solution, but not nearly close to what I know we could have delivered within 2 more days. At the end, it was just a "worked out concept" delivery.