Based on everything I've seen Bungie themselves say about 3oC, they have nothing to do with legendary drops. All the 3oC does is increase the likelihood of an exotic drop when completing activities that already have the potential to yield an exotic drop. They don't convert a legendary roll into an exotic or anything like that. So any time you get an exotic from a 3oC, it is because the activity you completed already has the potential to yield an exotic.

That's what they say yes, but based on lots of information collected by reddit users, it DOES seem to convert a legendary engram into an exotic (in PvE). I have rarely, (I honestly don't think I ever have) seen a legendary and an exotic drop at the same time with a 3oC. BUT I have seen 2 exotics drop probably 10 times from 3oC, and I've seen two legendary engrams drop at the same time without. Users on reddit noticed the same thing, if I can find the post about it I'll post it.

That logic doesn't make sense to me for a couple reasons.

Personally, I've had cases of double legendaries, double exotics, and a legendary/exotic split after completing a heroic strike, but not enough of any case to say that one is more common than the other. But setting that aside for a moment...

The way I understand post game drops is that you are given 2 separate "rolls of the dice" after completing a strike (hence the 2 reward slots in the post-game scoreboard). Each roll of the virtual dice includes the possibility of earning any of the items in the loot table for that activity, with different percentages assigned to each item. So, making up some numbers for example, each roll of the dice might have a 40% chance to earn a blue engram, 15% chance to earn a purple, and 5% chance to earn an exotic.
Since I get 2 rolls of the dice after each strike, it is theoretically possible (although highly unlikely) to earn 2 legendaries, or a legendary and an exotic, or even 2 exotics, without the help of 3oC.

Lets say for the sake of argument that while using 3oC, there are more cases of dual exotic drops than there are of legendary/exotic splits. If 3oC work by taking a legendary drop that is awarded by the dice and then "upgrading" it to an exotic, that means these players are naturally earning a legendary & exotic drop as rewards, the the 3oC is bumping the legendary up to another exotic. Yet statistically speaking, it should be impossible for a legendary+exotic drop combo to be more common than a dual legendary drop (because exotic drops are inherently less likely than legendary drops).

What I'm getting at is the logic here is false. If the 3oC work by taking legendary drops and upgrading them, that would not cause dual exotic drops to be more common than legendary+exotic combos.

What seems more likely to me is that 3oC operate exactly as Bungie has told us (minus the cooldown BS), and using them gives at least 1 of your 2 virtual dice rolls a higher chance of yielding an exotic. We don't know the actual numbers, but 3oC could conceivably bump the drop rates for exotics up to or above the rates of legendary drops, which would explain why dual exotic drops with 3oC are more common than legendary+exotic or dual legendary drops.

My head hurts, lol

I do get that required first one per week, I should've mentioned that--if THAT ever fails, then I'll ram my car through their front doors. ;-)