That's not actually what it says.
The real synopsis:
UK Fact Checking organization says, "Um, we don't think the backfire effect is as large as some people say, besides, the research is American, and we're British."

Misinformation: susceptibility, spread, and interventions to immunize the public - Nature Medicine
This Review provides an overview of the psychology of misinformation, from susceptibility to spread and interventions to help boost psychological immunity.

Generally, the overall evidence is that there is an effect, just weaker than the original studies ... and, of course, more work needs to be done. That said, it shouldn't keep you from attempting to correct misinformation, especially when the correction can appear close to (proximity both spatially and temporally) to the misinformation.