The only way this makes some sense, and I hate to invent storyline but I kinda have to, is if Stamets had lied to Culber, telling him that he had been receiving medical care in some manner from another doctor, and that Culber best stay clear because of the ethical dilemma. Then Culber could ignore Stamets being a little tipsy, under the impression that it was a psychological toll that could be healed when the war is over and the constant jumps aren't necessary anymore. It was only when he did his own scan did he see that there was possibly irreperable damage being done to Stamets brain.
And Stamets would also lie to the CMO or somebody, or at least imply in some manner, that Culber had been keeping an eye on his vitals. And the only reason he went to Culber when Lorca ordered him to sickbay was in the hopes that there wasn't anything physically wrong, and if there was, maybe Culber would actually keep quiet due to their relationship. Culber, being a good guy, did not play along with that (not that Stamets would tell him to, it was probably a mild hope).
And Stamets would also lie to the CMO or somebody, or at least imply in some manner, that Culber had been keeping an eye on his vitals. And the only reason he went to Culber when Lorca ordered him to sickbay was in the hopes that there wasn't anything physically wrong, and if there was, maybe Culber would actually keep quiet due to their relationship. Culber, being a good guy, did not play along with that (not that Stamets would tell him to, it was probably a mild hope).