My guess is that the P12 ultimately tries to remove the case to California federal court. P12 HQ is in California and I assume there's a venue clause in the bylaws.
I think the purpose of the filing is not to stop all activities just any opportunity for any vote to be taken that would impact P12 finances. WSU/OSU do not a meeting to be held, whether designated a "board meeting" or not, where the other schools can vote to void any exit fees, disburse money, allocate NCAA credits, or the like. WSU/OSU want to get some temporary ruling to stop Kliavkoff from calling any meeting of any sort.