I suspect those lying down on the job need more/ better waterproofing than upwrongs as a greater area is exposed to vertical rain.
For a start, unless you're following someone with a naff mudguard your feet tend to stay drier, as they're clear of the front wheel and gravity isn't delivering water from the rest of your legs, so you're generally winning there. Of course, if you've got a front fairing, your feet and legs should stay totally dry (though your face will get a nice soaking with every pothole).
Waterproof jackets are annoying on recumbents, as they don't ventilate properly, and as well as the traditional puddle (or collection of hail stones as I had last month) on your tummy, you can end up with interesting failure modes like puddles of sweat forming at your elbows. They'll also thwart whatever ventilation your seat has.
But recumbents put you in a more aerodynamic position, and even the best ventilated seats act as a layer of insulation, so you tend to dissipate less heat than on an upright. My preferred strategy is to keep clothing to a minimum, get soaked, and only add waterproofs when I actually get cold (which I will as soon as I stop). Putting on waterproofs is only going to soak me anyway. So you're right in that I'll need to carry layers that I might be wearing in the same conditions on an upright.
What's probably needed is a body equivalent of rainlegs...
(And of course the 'vertical rain' thing is a fallacy. It's always a headwind.