Does this reasoning also apply to a team's new GM who's inherited bad contracts?
As far as culpability for the error, no. Yet a GM in this situation is still asking the owner to bankroll a buyout/retention decision at a time of belt tightening, when who knows how long it will be until paying fans are in attendance. That's a tough conversation.
Most owners will prefer that their GMs make it work without exceeding the salary cap, if not a little lower for a while. There are fluctuations in which payroll dips above and below the actual cap due to different contract structures, but the principle still applies. Owners are going to favor frugality and making sure their teams are maximizing performance per dollar for a while, not taking advantage of every CBA provision that allows teams to buy their way out of cap jams.
Concocting a plan to pay players not to play for you is no way for a GM to get into the good graces of an owner. That applies whether the GM in question signed the player to the contract or not. Most owners are going to consider a good job on the part of the GM making the payroll work with those contracts still on the books (if not moving them when feasible - however unlikely in the case of some of the league's truly dreadful contracts).
My suspicion is that most GMs just implicitly know not to go their owners with these kinds of buyout proposals. Many owners will ultimately agree if the GM presents this as the only way, but they do so grudgingly and the GM is losing face in this scenario.
