Beef is the most popular choice of meat used in the filling nowadays by butcher's and baker's alike and the seasoning consists of a bit more than just salt and pepper, so I wouldn't hang my hat on that BBC recipe.
Also, adding some water to the mix makes for a far more succulent tasting pie.
There's no need to glaze the pie lid's unless of course you're using puff pastry - but no self respecting traditional scotch pie maker would be daft enough to do that anyway.
Soaking the lid's in water for a few seconds just before use means they'll adhere better and stay fairly soft during the baking process, preventing the risk of them coming out of the oven brittle and dry.
