Why is an alkoxide released instead of hydroxide in the attack of trialkyloxyborane by hydroxide?
Both hydroxide and alcoholate can be displaced from the tetracoordinated intermediate. The difference is that displacing the hydroxide is just the back reaction of the inital attack while displacing the alcoholate will move the reaction forward.

You cannot argue that $\ce{X}$ is a stronger base than $\ce{Y}$ and therefore $\ce{X}$ will always get displaced. At best, you can argue that $\ce{X}$ is ten times stronger so the probability of $\ce{X}$ begin displaced is higher than that of $\ce{Y}$. For all intents and purposes of the argument, the basicities of (primary) alcoholates and hydroxide are too similar to make a real difference.