Correct: as far as I understand, the SCTA/BNI will only sanction record attempts at their venues (cloning the FIA rules to keep credibility) and as far as I can see don't want to be officiating at any other place. By "taking over the administration of world record attempts" they probably mean at their venues.
Basically, while they will recognise FIA records, they won't have nothing to do with FIA, and will develop their own list. For them, it has been a headache to work with the FIA and they had to respond to their members views. Mentioning FIA around Bonneville pits can raise a few smiles or long horror stories!!
What others want to do if they choose not to run at Bonneville is their business. Probably like in the past, arrange their attempt with a national FIA affiliated club and go through the whole process on their own: the survey of the course, the timing equipment, provide staff, medical cover, etc... and of course 'invite' a FIA official at great expense. They could find a place in some deserts, or an yet untaped new location, or go to Lake Gairdner, or some remote place in Mongolia, or try on an airfield, or a stretch of closed road, it would be for them to decide. They would have to hire locals to prepare the course, organise the logistics, transport all the equpment, find a surveyor, time-keepers, medical staff, etc... (Noble has done that twice for his jet records, at huge expense)
They could do all that or they could do their figures and decide that it makes sense after all to come to Bonneville where everything will be ready and run under SCTA/BNI sanction! Weather conditions apart, they are guaranted to run with an experienced organisation among people who know about record attempts. Bonneville is still good for at least 500+ mph, and there are not many speed record contenders that we know who aim higher at the moment.