While they were talking alone(mc and 89) the mc found out that she is a yandere imoutocon dungeon destroying queen(both meanings). Since she is not an enemy of rokuro he figured there is no harm for the dungeon to have contact with her. Plus he would get dp from the battle and he would use that so he can prepare a great pillow for sleeping. This is also a chance to get information about this world from someone who knows what is happening both above and underground(on the surface she is a high ranked adventurer and below she spread misconceptions about dungeons, also she is the founder of a HUGE empire. If he refused he would have to collect the information himself lose an ally to support the dungeon and if he gets on the badside of 89 killed.
quote from the novel “It’s alright, even if the master dies, the core will be fine.” so no lost for rokuro. Frankly the only reason he is not dead since 89 feels like this guy can help rokuro. The dungeon battle is a test on how much.