It would be interesting if active neurons were suppressing memories but I don't know of any evidence in support of that idea.
Most of the articles cited by the author don't deal with neurons that are directly involved in memory. The articles described the activity of neurons in primary sensory areas: the neurons in cortex that receive direct input from the periphery, or at least are the closest to neurons in the periphery in terms of number of connections between them. One exception is the article she cites about the hippocampus, but this area is required only for forming memories--once the memories have formed, they live somewhere else, but probably not in the primary sensory areas. Okay, maybe memories are a distributed network that includes neurons in primary sensory areas...but it would be weird to also have the main sensory area also be the place where memories live.