Full stack testing was not cutting corners. After ground testing it was deemed that incremental testing would not be beneficial. Doing tasks in parallel instead of in series can introduce project risks, but that's not the same thing as cutting corners, which is where something necessary is not done at all.
The idea that rocket X not exploding in a single launch makes it man-rated is cutting corners.
Full stack testing was testing the entire rocket at the same time instead of using dummy stages to test parts of the rocket separately. There was opposition to it because if the rocket failed it might be difficult to diagnose why exactly it failed, which would slow the project down in the long run. Based on the ground testing and advances in instrumentation, the risk of a project delay from a failure was considered acceptable. It still took multiple launches to man rate the rockets. There's a reason the first manned launch of the Saturn V was Apollo 8.
After the fact, it always looks inevitable.
Would you have gone up on that first manned Saturn launch? Not me. Recall how the space shuttle was safe, until it blew up. And then it was safe again, and broke up on reentry.
Everyone on the first manned Saturn test died. Do you know why people got into the second manned test? It was not that they knew with certainty it would be safe, but because they thought it was realistic that they could accomplish their goal.
People die in car accidents every day, that does not make my plan to drive to work tomorrow unrealistic.