This is a great piece of information. Usually it's frustrating to try and pray only to find your thoughts wandering aimlessly somewhere in the middle of Tefillah. At least now we know this isn't a failing on our part, rather it's part of the system of prayer.
I think the two reasons Rebbe Nachman brings down are actually the same reason, and its a question of how you look at it. On the one hand you can distract yourself from these distractions, and focus on legitimate tefillah, in which case as far as you're concerned the thoughts came (for reason #2) to distract you so that you may prove your worth by ignoring them.On the other hand, if you choose to raise these thoughts up then you can roll even these seemingly unrelated thoughts back into your tefillot, in which case they came back to you for (reason #1) you to fix.
Now, rather than thinking you've failed by being distracted in your tefillah, you can view it as a new challenge to overcome, so you can take your tefillah deeper.