Everything works fine, even adding new items, but if there are no previous items (i.e. the new editing row is the first row in the collection) then the the new row is deleted right after its creation (when creating a new row after passing the The DataGrid.InitializingNewItem event handler, the ObservableCollection.CollectionChanged is triggered one more time reporting a Remove action. I didn't manage to find out who makes the new row to be deleted.
This question might be a little subjective as I am pretty sure it's my fault in one part of my code, and I regret that I can't post my code as it's really large amount of code and it could be every line; I am just looking for a way to debug it and locate the source of the deletion of the newly added row, so I can fix it.