I actually wouldn't chance it because the fertilizer goes down into the ground so even though you are taking the grass from the top, the fertilizer can still be around the roots.
OK so then what I am getting from what everyone is saying is that don't use anything from the yard at all. Can the fertilizer from a neighbor really affect my yard too? Or is it just that everyone is being extra cautious? What about buying the grass in seed form that is sold for cats, can they eat that? I think it is wheat grass......