That's the part I disagree with. If he would have had a good/great season for Arsenal then I don't think 20m was too good to turn down. Playing at his best, or near it, he could very well be the difference between Arsenal being a top-4 side or not. One year without Champions League is more or less worth 20m in prize money alone (assuming they could reach the final 16), let alone if you consider all the other non-financial implications of being out of the competition, such as the ability to draw talent, match-day revenue lost, etc.
This can only be considered a good decision if we assume he'd be shit for them this year.
Granted they may still reach 4th without him, which would make my point bogus, but I don't know if it's justifiable for a club as wealthy as Arsenal to put themselves at so much risk for 24m.