Very much agree. It's a pretty common mistake to bundle real information with obviously wrong details and lose credibility. Especially in the eyes of people looking for a reason to discredit the argument.
The disingenuous people who discredit climate change will do so no matter how serious people act. There is no point in changing behavior on their account.
The point is to convince people who are undecided. Using information that's known to be false or weakly supported is then short-sighted and counterproductive, because enough false predictions will turn up that those undecided will tune out entirely