Ignoring the damage output from the combo, my point: Edna can 2TKO Rapp.
Rapp (G1) vs Edna (SH3) - Water resistance and speed really **** Edna over here I think. As it means Rapp should only need to heal once after Edna's combo, and also buys him the time to get a Speedy or two off if need be. 3 Demonballs and a Meteor Strike or two should be enough to KO. (3 DBs alone are around 110% kill damage.) He also has a fire based move/skill (Fireball) which could work really well here in the place of DB, and he has the SP to use it 4 times. Though i'm not 100% sure what I see its damage at, it's at least more powerful than Missile. (Missile being considerably lower level and SP use.)
Even you said that Rapp can't 2HKO back.
It essentially boils down to this:
Turn 1: Rapp -> Demonball
Turn 2: Edna -> Black Hole
Split
Turn 3a: Rapp -> Demonball or Neo Demonball, it doesn't particularly matter
Turn 4a: Edna -> Double: Physical -> Black Hole, win
Turn 3b: Rapp -> Heal (less than full)
Turn 4b: Edna -> Black Hole (go back to step 3b until Rapp has less than 81% health even after healing)
Turn ?b: Edna -> Double: Physical -> Black Hole, win
Essentially, while allowing Mana Egg skills, Rapp has to fulfill the following conditions to win:
1) Have at least 41% (or higher, I'm not entirely completely sure on the speed difference between Edna and Rapp) healing magic that doesn't slow him down at all.
2) Get enough doubles where he can kill before he is killed himself.
From what little information I could get in terms of research, he has 95 uses of Heal, and 23 uses of Healer, if you allow him Mana Egg skills outside of what teaches him his weapon skills.
Another aside...
1) Rapp is game best speed, Edna is below average. (the stat topic lists her as being "slower than Frank") I don't remember her recharge being that big an issue. It was fast, but nothing special. Not enough to overcome the disparity in speed.
It's possible that OK was just eyeballing speeds while trying to get other numbers. Dark Holy Elf noted later on in the topic that Edna actually has 26 Speed (as opposed to Frank's 24), and that all non-Lady/Umbral bosses have that Quick Hit property to their attacks, but possibly slower first turns.