Of course it's correct, but these mental mathematics also prove that to people like
@BluesJr the rise of Chelsea/City/PSG/whoever was never about the source of the money despite that always being used as a stick to beat the clubs with.
Even though the intentions were always masked with some moral/ethical ramblings, with the fans of the more traditional big clubs it was most of all about just feeling threatened that a new kid on the block dared to challenge the status quo of the old elite. And with fans of the smaller clubs it was mostly jealousy I guess?
Whether a club has been successful in the past or not has absolutely feck all to do with the intention of sportswashing by the bloodthirsty ME-regimes. Either they'll spend less money on buying the club and more on building it up, or they buy a top club with ready-made global fan base for billions and then just spend whatever's necessary to get them back to being competitive. Either way the goal is to shape the opinions of people around the world and clearly they're about to be very successful when they haven't even bought the club yet and people are already defending them.