This is an amazing story.
I also suspect the problem might be coming from subs in the neighbouring country attempting to register on your network…but then I have a problem with this theory.
During Cell Selection/Reselection, isn’t the MS supposed to select an “allowed” PLMN? If there is no “allowed” PLMN and the MS selects another PLMN(your PLMN in this case), it is supposed to go into “Limited Service” state, isn’t it? In this state is the MS allowed to request for a channel on a PLMN which is not “allowed”?
I would suggest you visit the border of your country and buy a SIM card of the neighbouring operators and doing a test registration on your PLMN. If the MS is allocated an SDCCH, then you can conclude the problem is coming from the foreign MSs.