Hmm is that true? I'm not sure about that because after server merge for my server (which was around Jan) I always received 1/4 of what I was used to because there were 4x the number of players and proportionate amount of high dps'ers from each server merged. Ninetails by itself, from what I have observed, didn't get stronger or weaker immediately - it did seem to level up faster though - but the amount of coins/xp I ended up getting were the same over time since players were also powering up proportionally. But I could be wrong here, feel free to let me know!
I believe it buffs itself if it dies under 4 min and nerfs itself if it takes more than 10 min, so there is some leeway in there. But at least for my non-merged server, I have seen it self adjust a number of times after a quick/slow finish. In fact, just last week it went from 45m(or is it 450? I only care for the first 2 digits XD) to 68m to 48m. It had been 45m for about a month, 68m for two or three runs after a surprisingly fast finish and then dropped after a slow finish where 2-3 of the ptws who are usually in top 3-5 didn't show along with some others.
Do note, however, there is a different modifier based on ranking as well, I believe 1st place is 150% versus 16+ which is 100%, so you could lose up to 1/3 of your reward even if you dealt the exact same damage from that. And given the leeway in the time, 10 min to 4 min would be a loss of 60%. and 40%*2/3 is about 1/4 (4/15). So indeed, under the worst possible cir*stances, you could drop to 1/4 income even if your damage stays the same.
So I guess technically speaking, yes, you can gain more, but that's only so if your server fox damage is surprisingly stable and happens to go from 4 min to say 8 min so that the readjustment is not triggered from the loss of people. If it does trigger, then the gain is gone and it might be difficult to get it back.
But then again, being once per week, it would be "normal" on Thursdays but causes the Firday fox to be weak, and potentially be back up to normal for Sunday after a fast Friday, so the amount of loss/gain would be rather complicated.
But if your server was finishing in say 6 min regularly, it gets nerfed due to running over 10 min on the quiz day but not by much such that "other" days end up being say 4 min 30s so it doesn't get buffed back up... well, in that case EVERYONE loses out. This is the worst case scenario.