Noctem
Explorer
The disintegrate spell says "If this damage reduces the target to 0 hit points, it is disintegrated."
The Wild Shaped druid is hit with disintegrate. Takes damage that reduces his animal form to 0 hit points, and is disintegrated.
A disintegrated creature is dead. "Die" is one of the things that triggers reversion. So, the dust is Druid dust, not animal dust. Hooray! As a result of reversion, at least the Druid's magic items are recoverable.
Think of the order of operations like this:
Work At Disneyland: while you work at Disneyland, put on a Mickey Mouse costume. You have to take off the Mickey Mouse costume and get back into your regular clothes if your costume gets wet. If your costume gets dirty, your boss fires you. Someone throws a bucket of mud on you. Now you're wet. So you have to change out of your Mickey Mouse costume. But you're also dirty, so you're totally fired immediately.
Work at Disneyland = wildshape ability. Wear costume = animal form. Get wet = Reach 0 hit points. Get fired = disintegrate.
In other words, in the above example getting wet and getting dirty both happen--they're inextricably linked--and both consequences apply.
Same with reaching zero hit points from disintegrate. The spell's damage reduces taget's HP to zero, so the target is disintegrated. That happens. The target was a wildshaped druid, and wildshaped druids revert when they die. So the (dead, pile-of-ash) druid reverts. That happens.
The Target was a wild shaped Druid. WAS A WILD SHAPED DRUID. The wild shape IS the Druid. There is NO FORM LEFT, as the wild shaped form, which is now dust, was the Druid. The wild shape is not a shield, it is not a battery of hit points FOR THIS EFFECT, the damage itself is what is irrelevent - if the disintegrate does enough damage to make the wild shape reach zero, then as per the spell description, the form turns to DUST, there is nothing left to revert to a Druid. DUST will not revert to anything.
Sorry but you're both wrong via the rules in the PHB and because Jeremy Crawford has directly stated as much. So if you want to houserule at home that this is how it works, go for it! But don't bother going online and trying to tell other people that your houserule is how the game is meant to be played. That's not the case at all.