The reasons are many for USC not wanting to deal with any P12 school. And the biggest reason is - the P12 itself. I have family members that went to USC and a friend who works in Administration at SC. The main reason they cite is that USC Admin and alumni felt that the media deal negotiated under Larry Scott, and historically speaking, did not account for SC's contribution to the value and prestige of the P12. They had always felt that they had "carried" the conference and brought the most value to the conference out of all the member schools.
I think recruiting and Oregon are also factors but I think they are less so with respect to USC not earning the dollar value they always thought they deserved from the P12.
I think recruiting and Oregon are also factors but I think they are less so with respect to USC not earning the dollar value they always thought they deserved from the P12.