Are you calling people “things”? Huh? Huh?

But seriously, though, the “seven things” is specifically the generic counter つ, which always uses the kun’yomi. For other counters, you almost always use the on’yomi (though there’s a few exeptions, of course – there’s always exceptions).

That said, 七 is weird in that its readings can be fairly interchangeable (though usually not when attached to a counter). ななにん is also a valid reading (it’s used in the title of 山田くんと七人の魔女, for example).