You put artificial limits on design exercises because engineers will inevitably continue tinkering forever if you don't. it's a consequence of engineering as a commercial pursuit, where schedule and budget become variables in the engineering management equation. The engineer wants to minimize operational risk by reworking the design. But it's more accurate to say you want a design that's just good enough, because better is the enemy of good. Often an engineer will have to defer to someone else's opinion of "good enough."
I think it's more helpful to look at the test regime. While designs are locked down at a certain point, acceptance and flight qualification test criteria are locked down even earlier -- in the requirements analysis stage. The contractor and the customer agree on what criteria will need to be met in order for the contractor to get paid, and for the article to be ready for flight. In most cases the methods of testing will be agreed upon. Once set, these factors are hard to change. It's the same philosophy as engineering change management, in the sense that you don't want to enact some ad hoc change to a testing regime that ends up missing something important. So proposals to change the test regime have to be reviewed for technical validity. But from the business standpoint, neither party wants the other tinkering with the acceptance criteria. The customer doesn't want the contractor relaxing the standards, and the contractor doesn't want the customer to move the goalposts. Because there are both technical and business concerns at stake, changing tests is at least as difficult, if not more so, than changing designs.
I don't know if testing the thermostat trip behavior under load was actually on anyone's radar at the time, but it probably should have been. And if it was, it may have been working its way through the change management process. To answer your actual question, I would have to say a little of both. Whether the work product in question was the tank design or the testing plan, both would have been locked down fairly early in the process. And any proposed revision to them -- no matter how logical, important, or well-intentioned -- would need to go through a rigorous change-management process.