Just to be sure:
According to my dictionary, PVP means player vs player, so no team filled with bots. Matchmade means non-custom game mode, where the matchmaking algorithm sorts you into a team. Is it correct? If it is, then tell me, why the "matchmade games only, Do something in PVP games" missions never make any progress for ARAM? Its played by 10 living players (so its PVP) and its non-custom (so its matchmade).