Does the iodoform reaction form hydrogen iodide or water?
Your balanced equation is correct, both water and iodide (and iodide in water will be in equilibrium with hydrogen iodide) are formed in the iodoform reaction.

$$ \mathrm{CH_3COR + 3I_2 +4OH^- \rightarrow  CHI_3 + RCOO^- +3I^- +3H_2O}$$

The Wikipedia article that you mention, could have been written a bit clearer.  Specifically, there are two key steps in the iodoform reaction.  First, there is formation of the tri-iodo ketone and water is generated in this step.



In a subsequent step, the carbonyl undergoes an SN2 reaction to generate iodoform.



The Wikipedia drawing in your post seems to focus on the mechanism of the second step (3 to 4b).  The first step (2 to 3) is just illustrated in a cursory fashion and the formation of water is not included in the figure.