Transporting someone else's goods across US border

I'm a Canadian living in the US. My parents (also Canadian) are driving down to visit me and are bringing some furniture of mine down to deliver to me. A couple months ago they tried something similar and crossing the US border became a huge ordeal because the border guards said they weren't allowed to transport my stuff without me being there. My parents were told that there is some form they could have filled out to make this process easier; however, I can't find any reference to such a form online. Anyone know how to transport someone else's stuff into the US? Thanks!