It is and it isn't true. Light from the falling object will be red-shifted, and eventually you won't be able to see it, but if you could see extremely long wav

It is and it isn't true. Light from the falling object will be red-shifted, and eventually you won't be able to see it, but if you could see extremely long wave-length light, and if you could observe it for a really long time, you'd see light from that object asymptotically approach the universe's size as its wavelength, and you'd never see the object go over. But obviously it's not possible for humans to observe extremely long wavelength light, so you'd just see the object disappear when light from it red-shifts beyond the range you can observe. The object, meanwhile, does fall in from its perspective.