The linked source is incorrect in its conclusion (note that it cites 26 U.S.C. § 5801 which is irrelevant to its point). Hand grenades are indeed destructive devices regulated under the National Firearms Act, but they can be possessed legally. One must pay the ATF a $200 registration tax in order to purchase or build a destructive device. Note that a few states (e.g. New Jersey) prohibit the possession of destructive devices, but it is possible for civilians who are not police officers to possess them legally in the USA at large.
This [1] is the form that is completed to pay the $200 transfer tax when purchasing an NFA item. Note that this is the same form used to transfer machine guns (which are also legal for civilians who are not police officers to possess).
