Critical to have pointed this out. The suggestion that one should merely claim something back is fine. Anybody may claim anything. But, whether it gets paid is another.
There is not one word in EC 261/2004 or precedential court decisions which supports the proposition that one may use self-help and be reimbursed.
There may be times when self-help makes sense, e.g., when the price has dropped or when a similar or better route may be obtained at minimal cost where the risk of not being reimbursed is not a big deal.
But, it makes me cringe to learn of people who pay vast some to purchase new tickets, fully expecting to be reimbursed and then being denied and left with an expense which they cannot afford.