Can one enter Leomund’s Tiny Hut from below?

In a session today we were camped out in a Leomund’s tiny hut and the DM determined that since it is described as a dome, the bad guys (Wraiths, so they are incorporeal) could enter the area from below. I went with it and it was a fun encounter, but I wondered what other people think about it. I can see two arguments.

His argument: It is described as a dome. So only the semi-spherical outside prevents things from happening. A dome doesn’t (necessarily) have a floor, they can enter no problem.

My argument: The intent of the spell seems to be to prevent baddies from coming in. The rest of the wording simply talks about the “area”, not a barrier.

Has anyone thought this through or seen a ruling anywhere?

Note: Given that I’m playing a 3-foot tall gnome, we decided that on subsequent castings I’d do two. One is the normal one and the other is an inverted on with a “floor” about five feet in the air, that extends into the earth. The overlap allows for protection.