From the article: “To gain access to Waymo’s design server, Mr. Levandowski searched for and installed specialized software onto his company-issued laptop.” This implies to me that they did not “let him have access”, but rather that he had to circumvent company policy to get at the files.

Further, one can easily imagine that this statement may have been one he shared over lunch once to a set of coworkers, that it was not known by anyone in management until after he left, after they found the evidence of wrongdoing and interviewed people. (I have no evidence either way, but it seems unlikely that in any company an employee could say such a thing openly and loudly to managers and remain employed for long.)