What an anticipatory laughter Donaldson must have had at our expense when writing this scene! Well, it turns out that what would have been the very worst course for Frodo was the best for Covenant. It is not the same kind of Ring, not the same kind of magic.
The author suggests that the outcome of the scene, while initially appearing negative for Frodo, actually benefited Covenant in unexpected ways.  The rings have different characteristics and powers.