There's nothing wrong with our site. You simply had the wrong generation selected - you have to have GSC selected on the Learnsets page. The "show all" option defaults to RSE, FRLG, DPP, HGSS and BW. Also it's not considered an egg move on the site, it's considered "other" (you can't really list it as an egg move because it's obtained a special way, only the Odd Egg Cleffa can get Dizzy Punch, a regular Cleffa cannot learn it.)
So yes, the baby Pokemon you randomly receive from the daycare couple as an Odd Egg will know Dizzy Punch.