It doesn't really matter how Katara got drunk, in fact she has no idea how it happened, except she's certain Sokka is to blame somehow. What she remembers is the next morning. Being a waterbending healer of some renown, upon waking with an entire Fire Nation public school marching band tramping trough the inside of her skull, she promptly dunked her head in a bucket of water. Sokka's attempts at illustrating the scene for blackmail purposes, however, fell a little flat.