The OBi 202 has two physical telephone ports, not four. It only supports two different telephone wire pairs being connected. The Line 1 jack is a 4-wire, RJ-14 jack, with the standard US telephone wiring convention: Line 1 is on the inner two conductors, and Line 2 is on the outer two conductors. The Line 2 jack is a RJ-11, 2-wire-only jack. It has Line 2's circuit on the inner two conductors. This is typical for two-line telephone devices, as it allows the customer to either use two separate phone cords with RJ-11 wiring, or one cord with RJ-14 wiring.
You can direct any of the four service provider configurations to ring on either the Line 1 or Line 2 outputs.
The issue you have is fax detection. If you plug a fax machine into the Line 2 wiring, it, not the OBi, would determine whether or not it auto-answers calls. The fax machine would need the capability to answer all calls, and ignore voice calls when it doesn't hear the fax tone. This would still interfere with handling voice calls, since it would preclude that line from going to voicemail if unanswered.
What to do? Either buy another OBi and dedicate a phone number to the fax, or leave the fax's auto-answer setting tuned off, and manually turn it on when you know someone is going to send you a fax, or, use the more modern solution: get a fax mailbox. Callcentric, for example, one of the SIP VoIP providers easily configured on an OBi device, offers inbound fax reception to a fax mailbox. It can then email you the fax, instead of using the fax machine.