I hate, hate, absolutely hate, but really and truly hate time paradoxes. Because as it stands, Elizabeth would have learned the secret from dear old Daddy and theoretically should have known damn well who "cousin Barnabas" was when he came knocking on her door.
Personally I rather enjoy puzzling out the time paradoxes. However, such a paradox does not necessarily have to come into play in this instance. If Barnabas had not interfered w/history in 1897, one might suppose that Edith did pass the secret along to Edward. However, being the stuffy and pompous cynic that he is, Edward may well have shrugged off 'the secret' as the nonsensical ramblings of an insane old woman and thought no more of it.
And even if Edward did learn and believe in the secret, he himself may never had the opportunity to pass it along to his son, Jamison. Perhaps his death was sudden and unexpected. Further, if he did pass the secret along to Jamison, it may have been Jamison who passed away without having the chance to pass it along to Roger or Elizabeth. There's enough of a gap between Edward and Roger/Elizabeth to still have lost the secret somewhere along the way.