I have very little experience with these vegetables as companions but I believe that FarmerLor has it right, corn plants in single file have trouble competing with the vines. At least, that was my experience.
And, what is a hill? Oddly enuf (

), I once researched the meaning of the word as it applies to gardens. Everyone thinks that "a hill is a hill." Perhaps the Iroquois gardeners did gather soil together in a mound to sow their seed. But, of course, the word is English . . . or is it?
The gardening term comes from the Dutch and, altho' it has a meaning nearly the same, it doesn't quite mean a "mound of earth" - instead, it means, more-or-less, a "mound of plants."
If we think about a flood plain (like along the Rhine River in The Netherlands), we know that it is flat, flat, flat. Okay, there may be dikes and canals . . . but taller plants will be noticeable and, apparently, identified as something different than the rest of the landscape. There are other words for "mounds of earth" in the Dutch language.
At least, that's how I remember it but I no longer remember where I got this information.
Starting with a mound of earth or not, allowing the corn plants to stand together helps with their growth and, no doubt, pollination. Seems to me . . .
Steve