Noob question about wireless printing.

I realized that when you connect your printer to your wifi, and enable wifi direct, it gets displayed to everyone. So say, someone connects to the printer, does that mean they could connect to my wifi network since the printer itself is connected to the wifi?
Apparently wifi direct is peer to peer; which means if I'm not mistaken, that information is to be transmitted only between two nodes, in this case, the printer and whatever device is connected to it, and that there is no intermediary nodes. But could there still be vulnerability?