Let's now consider whether the basalmost Euparaves were ground-dwelling or whether they were flying in the trees. Pedopenna, Epidexipteryx and the other flying primitive birds such as Eosinopteryx, Aurornis, Xiaotingia and Anchiornis etc were all flying in the trees.
So if the basalmost Euparaves were ground-dwelling, then they must all have BECOME flying primitive birds AFTER splitting from the dinosaur line. Not only that, but they must all have developed like that convergently, to become like the other flying birds that came later. That is not parsimonious.
The most parsimonious alternative is that the basalmost Euparaves were feathered, long-bony-tailed, flying primitive birds. And the ground-dwelling oviraptors and alvarezsaurids that came later, were secondarily flightless.
Pedopenna was originally classified as a paravian, the group of maniraptoran dinosaurs that includes both deinonychosaurs and avialans (the lineage including modern birds), but some scientists have classified it as a true avialan more closely related to modern birds than to deinonychosaurs.