They have to allow write access to some applications otherwise there can be no third-party address book apps. If there was such a permission, you can bet that facebook would have asked for it by default. You can also be sure that hundreds of millions of people would have granted it and we would be seeing the exact same problem.

The root of the problem is facebook. The important questions should be directed at facebook. We can look to Apple or Google for help, but ultimately when we install an application, we grant it our trust and Facebook routinely tramples all over it. Turns out that it's a winning strategy.