The $600 would get taxed when (if) the painter bought something with it. (Assuming, of course, that his purchase wasn't an under the table deal as well).
Yes the money would be taxed when the painter bought something with it, but it would not be taxed when the houseowner earned it.
The transaction not being taxed is the transaction from the houseowner to the painter, it really makes very little difference wether you are not taxint the transaction as painters income or not taxing it as houseowners expense.