Admitting that you have a broken culture will cause all your customers to question everything about the company, impacting sales, stock price, employment it could get ugly.
If he admitted that Boeing had a cultural problem he should be fired for being an idiot.
I'd like to better understand your thinking / background on this, as every case study I've ever read about crisis management indicates that you are better off being very vocal and visible about mistakes and at least superficially make it look like you are acknowledging the breakdowns and seeking to make reparations.
Their customers would need to be willingly ignoring facts not to be in the known by now. 2019 saw negative sales and the stock market is beginning to react.
Boeing decided it's business as usual when they had a chance to own up to some responsibility. I don't want to get into the details because I wouldn't make them justice, but the list is insane; from impossible engineering choices to brown envelopes (bribes) to the regulators.
They could have said something among the lines of "we are working on improving our processes to avoid future deaths", but instead we hear them blaming the pilots, again: "Calhoun focuses Boeing’s responsibility on faulty assumption around pilot response on MCAS".
As a reminder, MCAS could overpower manual trim and stick inputs. The crew never stood a chance, they were condemned the moment an engineer at Boeing decided it was ok to create a system like that acting on a single sensor that was known to be unreliable, and their process somehow allowed them not to test for its failure.
If he admitted that Boeing had a cultural problem he should be fired for being an idiot.