When the author say "we have no problem with you distributing our software through the app store", then I would just get that in some more official writing that include you, apple, and more detailed description on what permission is exactly given. The primary purpose of any software license is to shield the downstream distributor against being charged under copyright infringement, but a personal permission is equally fine in a legal sense so long you don't intend that downstream from you should also be able to distribute your version.