I actually think you are both right.
Parachute payments are needed because of the gulf of finances between the two leagues, so for a club going down it's a big hit (trust me, my club has seen enough of it), but they also provide an advantage to teams who have failed over those they will be competing with.
Ultimately the solution is to make it a far smaller gap in finances between the two leagues, that way you can remove the parachute payments and, at the same time, provide a more level playing field for all clubs in that lower division.
Some, not all. Hearts are there through their own failings despite having massive benefits over the teams around them. Their position is based on utter negligence not through "luck".