The issue with the dilution does depend on the poison.
If the poison is something that can be metabolized in very small doses, then diluting it will help b/c there is only so much liquid+poison that can be absorbed at one time. For instance, If you were to drink an entire gallon of water, you would not instantly absorb the entire amount of water within a minute.
Same with the poison. Imagine you were administering a poison that requires someone to absorb 20ml within 30mins on an empty stomach to effectively kill them (because it has the sustaining power of nicotine, so it is metabolized very quickly). Now imagine that poison is delivered in a tall glass filled to the rim with ice and then the rest is water. That amount of water may be absorbed within the alloted time limit, and the person would die. However, if the ice were to melt, and effectively triple the amount of liquid being consumed, then there is a less likely chance that the entire contents would be absorbed within the required time frame, before the metabolism would begin to eliminate the amount of poison already absorbed in the body.
That's about the best that I can put it. It depends on the strength, dosage, required dosage, rate of absorbency, and metabolism.
I don't really know how long nicotine lasts or anything, I pulled the numbers out of the air just for the explanation. I hope it's clear.