I didn't mean to imply that high Dps doesn't help. It does. Of that, there is no doubt, and you're definitely right that high dmg and mitigation are not totally exclusive.
As both of you pointed out, killing things quickly in dungeons prevent the need for Tanks and Healers from spending too much Mp or blowing extra def CD's, and burning Trial/Raid Hp bars quickly allows you to push phases, preventing additional dmg from repeated attacks as well ... but neither of these things are mitigation. They're prevention.
It's a bit nit-picky, but mitigation is actually taking the hit and mitigating it. Not taking the hit at all means that you're not mitigating anything. Further, in regards to Trials and Raids, specifically, High Dps might allow you to push phases faster, thereby skipping extra Tank busters, but pushing phases does nothing to help you mitigate the dmg you are actually taking. Skipping an extra Blade Dance is nice, but you still had to mitigate everything that came before. High Dps output does not change that you were using Def CD's. It just stops you from using more of them. Though, pushing phases in current fights is kind of a bad example, because there are long recovery periods after each skip-able tank buster that make extra CD burns irrelevant, and certain hits (like the 3rd H Blade Dance) are actually a mini-Dps check. If your team doesn't prevent it, you are highly unlikely to clear meteors.
Regarldess, you are both right. High dps is most certainly a big help in any fight. It does a wonderful job of preventing additional and unnecessary dmg, and thereby is essential for preventing unnecessary mitigation. However, actually mitigating hits is purely in the domain of Tanking/Healing. No amount of Dps will reduce the actual dmg you take from a hit. It might prevent additional hits, but it does not reduce the impact of the hits you actually take (except in extremely rare cases like Sacred Cross). This is why high Dps is not the "best mitigation." It's just extremely efficient.