This is always something that's baffled me, mostly since it seems totally counter to how the democratic process should work (apart from the fact that it seems totally petty). Does that mean that this resolution would have to be repealed in order for the FCC to make similar policies again? That sounds less like "never enact policies like this" and more like "now it'll take one extra round of voting before new privacy-related policies can be enacted".
Congress cannot make any law that Congress cannot unmake. Congress can, of course, prevent a regulatory agency from doing something, because the regulatory agency's power to make law derives from Congress's delegation of that authority to the agency. (I'll leave aside the discussion of how that's totally unconstitutional.)
