Well, if you land in such a way that the helmet hits cleanly / squarely, then it'll do it's job, assuming it's legitimate DOT - that is, not just a DOT sticker slapped on.
And, what means 'skull helmet'? Are you meaning a 'standard' 3/4 open-face helmet that covers the sides / back of your head basically the same amount as your full-face? Or a little 'beanie' helmet which more or less perches atop your head and doesn't really come down past your ears? Or ?
The real thing, of course, is what if your head hits sideways or you land on your face? In that case, you might as well depend on your haircut or your sunglasses to save your head.
Just do the crash in your imagination - if your head lands in such a way that the 'edge' of the helmet hits the ground, then there's only that small contact area available to 'spread' the impact and be absorbed within the helmet's inner shell. As compared to, say, a side- or rear- or face-impact where there's a larger area for the helmet to spread the impact over.
I think your co-worked was over-simplifying things to say that it won't do ANYthing... But, IMO, in anything less than a clean/square-on impact, it won't do nearly as much as a full-face, or even an open-face type.
Kirk