I cannot think of any reason why it would make water poisonous UNLESS the container is composed of a substance that can be broken apart by sufficient heat to boil water and release other toxic compounds into the water. Presumably these would accumulate the more times you boil the water or the longer you boil it.
Boiling is simply the addition of energy, usually in the form of heat, to liquid H2O. At 100°C or 373.15 K that energy is enough to excite the H2O molecules to the gas phase, which we would call steam. Applying heat causes a PHYSICAL change, not a chemical change, so, other than the effect of heat on body tissue, it will not hurt you. Boiling it twice doesn't change anything. I would be curious to see where you read this.
As I've said, the only mechanism I can think of that would make water toxic would be that the addition of heat AND another chemical would cause a reaction to occur, either creating a new compound (H2O + MoleculeA --> Toxin) or releasing molecules into solution in the water.