Breastmilk is about 80-90% water as it is, so there really is no need to add additional water to it. Water use is also discouraged for the reason you used it: newborns can fill up on water, so they should not be given water. (It's like filling up on cookies instead of an actual meal. Their growing bodies need good nutrition.)
Your wife is correct that water intoxication can happen in infants.
Too much water dilutes sodium in the blood and flushes it out of the
body, thus altering brain activity, which can lead to a seizure.
Infants under 1 year of age may be more prone to these types of
seizures than older children because a young infant’s diet does not
contain enough food sources to replenish the lost sodium. Also, an
infant’s immature kidneys cannot flush out excess water fast enough,
causing a dangerous buildup of water in the body.
Certainly avoid adding water to breastmilk. Typically, water is not fed to infants until they start solids/baby food - and then too, it is supplied with meals. Once they are weaned off, water intake is increased to compensate.
I'd recommend keeping some back-up formula on hand, or even a soother to get relief from the sucking motion. Also try distracting the child until the mother returns, rocking him, etc. Don't use cow's milk as that also doesn't have sufficient nutrition. Stick with breast milk or infant formula.