They said they were "gutted" about the charges.
Preston told Fairfax Felyx had been climbing on the logs when they fell on him.
She said she had taken Felyx to visit his dad at work when the accident happened.
"He climbed up, and I told him to get down before he fell, so he climbed back down again," she told Fairfax.
"Then he turned around and climbed up one, and that just sent them all tumbling down."
Preston described how she and Hatherley desperately tried to rush their son to the hospital, but he was pronounced dead a short time later.
No criminal charges were laid by police.