Apparently, among those who don't eat gebrochts during Pesach, the custom is to specifically eat it on the 8th day. From http://www.chabad.org/holidays/passover/pesach_cdo/aid/265990/jewish/Gebrokts-Wetted-Matzah.htm:
On the eighth day of Passover, which exists only outside the Land of Israel, the gebrokts stringency doesn’t apply, and all feast on matzah balls and matzah brei, and dip their matzah into soups and salads. In fact, many have the custom to try to eat their matzah with as many liquids and wet foods as possible.3
The simple reason for this is that the celebration of the eighth day is of rabbinic origin.
So what? I've learned, and Wikipedia agrees, that the second day of Yom Tov is just as strict as the first.
If the reason for the custom is that we are concerned that the matza isn't fully kneaded and can become chametz upon contact with water, why are we not concerned on the eighth day?
I am interested more in answers based in halacha than chassidic ideas.