if the road surface is smooth and/or there is a film of something other than water present then you can indeed start sliding around like nobody's business.
In essence, for good grip in the wet you need the road and/or the tyre to be rough in some way.
Jobst Brandt's tests are often cited as evidence that 'slick tyres have plenty of grip in the wet' but an oft-missed feature of those tests is that he was riding on nice clean grippy tarmac (equivalent to if not actually) shell delugrip, which had rainwater on it, but nothing else. My experience is that if you ride round the UK on low pressure slick tyres as if the conditions are like that, it will not be long before you end up on your ear, because they are not....
The conditions for a full aquaplane are 'no contact at all' between the tyre and the road, at which point you have no ability whatsoever to brake or steer. Needless to say you can lose a substantial amount of grip well before this, and this can be unsettling or dangerous; on a bike you don't need to have a full aquaplane to have reduced grip and a skid, so the arguments concerning aquaplaning are indeed somewhat specious.
IME with wide-ish slick tyres at low pressures there are plenty of situations that risk a nasty skid and worse yet, the transition from 'some grip' to 'not enough grip' can be very sudden. Treaded tyres can have lower levels of grip under some conditions (eg in the dry) but generally break away in a fashion that allows more warning.
Things to look out for when riding low pressure slick tyres
- worn out tarmac
- overbanding
- manhole covers
- spilt diesel
- 'road film' (containing oil etc in summer or road salt in winter)
- mud
- green slime
- wet leaves
etc etc
None of these things is always very visible when the road is wet and in fairness you are likely to be in trouble on treaded tyres too. But IME the trouble will be less bad and the onset of trouble will be clearer to you.
If you have narrow tyres at high(er) pressures they will push through any given film of crud more easily too, so there are certain conditions where you will get more grip that way, too.
In the case of slick tyres the contact pressure (on a slick surface) simply defaults to the tyre pressure. In the case of treaded tyres the contact pressure can be higher than the tyre pressure so again the tyre can push through a layer of slime or w.h.y. more easily.
FWIW I will happily ride in the summer on wide low pressure slicks, just taking extra care when conditions are poor. In the winter I prefer a treaded tyre if it is wide or a narrow tyre with higher pressure in it (which can have less tread but some is still better than none). Even a simple file tread on the tyre shoulders (as was long-favoured for racing) gives more feedback when cornering in the wet and of course doesn't slow you in the slightest in a straight line.
cheers