When making a Privileged Attack, the rules say that no one else can "interfere" with it. "Interfere" is defined by the rules as spending money from your Illuminati group to aid either side. Can the attacking group and the defender group still spend money during a privileged attack? Can their respective Illuminati?
Yes, the attacker and defender groups and Illuminatis can spend money during a Privileged Attack. A Privileged Attack only means that external parties are forbidden from interfering.
I think you can justify this solely by reference to the traditional usages of English words: you don't "interfere" in your own attack on someone by bringing more resources to bear; neither do you "interfere" in your own defence by using everything in your power to defend yourself. To "interfere", both generally and also in this specific case, means to "intrude into the affairs of others". Attacker and defender are not "others" in this case, and can get involved in the struggle to the maximum of their ability and financial resources...