Bottom few inches of drywall got wet, but wall looks fine. Do I have to replace that drywall?
If you started mopping up the water right away and limited the water under the wall you should be alright. There's usually a small gap between the drywall and the floor so that would help in the drywall not absorbing a lot of water.
Now if the water was an inch or two deep and soaking into the drywall, then you've got a problem because the strength of the drywall would be compromised. You'd probably want to replace it.