How was Vegeta able to be revived by the Dragon Balls? (I couldn't find a question like this, if it's been asked before then please remove it.)
There are several known plot holes in the DBZ story, but one that interested me is that in the Buu saga (in DBK it's in ep127) it's said that when a human/alien that killed too many innocent people is dead, in hell they erase his body and his memories and recreate him. Piccolo said that in response to Vegeta's question of whether he could be meet Goku again, but it very clearly that he still won't be revived by the DragonBalls because of that.

The content of Vegeta and Piccolo conversation in DBK ep127 (translated from japanese):

Vegeta: Tell me just one thing first, in the Next World or whatever it
is, after I die, will I be able to see Kakarrot again?
Piccolo: At a time like this, it won't do any good to offer
consolation, so I won't mince words. That won't be possible.
Vegeta: (blinking in shock)
Piccolo: You'v killed to many innocent people. Once you die, your body
will become nonexictense, and your soul will be sent to a world
different from Goku's. There, your soul will be cleaned, and your
memories erased, and you will be turned into a new life form.

Now, in the original DBZ they created a plot hole by including a scene of Frieza, Cell and other villains watching the battle against Buu on earth when they were in Hell, but I'm not talking about that.
During the Frieza arc, Vegeta was clearly evil. Though he joined forces with Gohan, Krillin et al, he still killed a whole village, he's clearly evil, and yet, when Kaio asked Shenron to revive all the people killed by Frieza, Vegeta came back to life (in DBK it's ep51). If we go by the assumption that evil people are recreated in hell, then how was he revived?

Though for a fact that Vegeta asked at the end of Buu saga from Prolunga to bring back all those who died except for any evil people to unrule bringing back Babidi and Dabra, that's not contradict the above, since Piccolo specified specifically that Vegeta killed to many people so he won't have a body, unlike Babidi that was evil but didn't were just evil and didn't killed anyone (not by himself at least) and Dabra who Daio sent to heaven. it's clearly that there's definite different between killing a lot of people to be just evil - killing a lot of people contaminating the soul so it needs to be recreate (like Uub) while being only evil not.
Now, I know it's a fact that Toriyama didn't want to make the Buu Saga, and there could be plot holes and all, but is there still some explanation for that?

Note 1: This question came to me after watching Dragon Ball Kai. If in the original DBZ it's not a question, I would love to be enlightened.
Note 2: I'm reffering only to DBZ manga canon material, so evidences from DBS aren't related.
I'm not sure if I understand your question, but are you asking why he was revived because he was supposed to be erased? They explicitly mention in the series that Enma Daio Sama decided not to erase Vegeta's soul just in case he needed him for a battle. So what Vegeta said in the screencapture you posted didnt apply to him due to an Enma Daio Sama decision
Enma Daio Sama decides to keep Vegeta soul intact in case he was needed for a battle
(Sorry, I couldnt find an english version for this video, only a spanish one, but you can use the english subtitles feature of Youtube to add them)