This statement was at the top of TIL, but the claims in the comments for why didn't seem to offer good evidence, or used Egyptian law to back it up. Or is this claim just false?
Seems to be spurious. Here are all the lines of Hammurabi's Code (L. W. King's translation) which relate to drinking:
/108. If a tavern-keeper (feminine) does not accept corn according to gross weight in payment of drink, but takes money, and the price of the drink is less than that of the corn, she shall be convicted and thrown into the water.
/109. If conspirators meet in the house of a tavern-keeper, and these conspirators are not captured and delivered to the court, the tavern-keeper shall be put to death.
/110. If a "sister of a god" open a tavern, or enter a tavern to drink, then shall this woman be burned to death.
/111. If an inn-keeper furnish sixty ka of usakani-drink to . . . she shall receive fifty ka of corn at the harvest.
So yeah, nothing about watering beer down.