The Obi has the same "call screening" feature that chat has in Gmail, which is different from that of your other phones listed as forwarding phones.
Chat, and the Obi, only have the option to accept the call or send it to voicemail. Your Obi presses the 1 for you (which is why there may be a 1 to 2 second delay when answering calls on the Obi) and you can change that setting here.
Voice Service -> SP1 Service -> Calling Features -> XSkipCallScreening
to enable, check the default box on the right.