I think that the new book Champions of Corruption contains an error. Concerning betrayal feats, it says (italics are mine):
Characters with class abilities granting allies access to teamwork feats (such as cavaliers or inquisitors) can select these teamwork feats normally, but allies who are granted these teamwork feats can use the feats only as initiators, not abettors.
This does not make sense: the inquisitor has no ability granting allies access to teamwork feats. He only has the class ablity solo tactics, granting himself teamwork feats (as the name already implies).
Of course, cavaliers do have such class abilities (the tactician abilities).