If you read this so called fact sheet very carefully, you may have the following interpretation: Do not go to your home country while your asylum case is pending. This action will always haunt you even if you get your green card. The document clearly does not say that you cannt visit your home country after having a green card. It clearly says that you cannot visit home country if your case is pending because there may be grave consequences even if you were successful in getting your green card. Is it far fetched on my part?