If we remember back to "The Stories We Tell" then Daisetsu and Shoju both have very similar philosophies about the truth. Also from past fictions we've seen that Daisetsu has become more practiced in being very careful with what he says to people. Clearly after this fiction if any of the emperor's children should be considered capable of manipulation and deception it would be Daisetsu. Sotorii is pretty much an open book. Now put Daisetsu and Shoju on the same team... Sounds like we are in for some fun
That said I'm not sure I believe that Daisetsu was setting his brother up here. I got the feeling he was just legitimately tired of his brother's crap. Then the events of this story taught him that he really needs to be more careful with what he says since there can be very real unintended consequences to his actions.