We assume they are the same because we know that the H+'s and OI's are coming from a single reaction.
Although this is correct to call it an assumption because we know H+'s don't only come from that reaction in a solution, as there are small contributions made by the self ionisation of water. However, at 25 degrees celcius, we know that this contributes only 10^-7 moles of H+'s in 1 L of solution which is small enough to neglect.
With the question regarding "10^-14 rule" I think you are asking why it works for OH- and not OI-. It is actually somewhat complicated. When you are finding [OH-] using that value, you are focused on the effects of the production of H+ along with the consumption of water on the position equilibrium of the self ionisation of water (reducing OH-) and it does not actually concern the ionisation of the acid.
If this solution was at 25 degrees, we can indeed apply the "10^-14 rule" to find OH-.