Whether gravity is quantized remains an open question. To shed light on this problem, various Gedanken experiments have been proposed. One popular example is an interference experiment with a massive system that interacts gravitationally with another distant system, where an apparent paradox arises: even for spacelike separation the outcome of the interference experiment depends on actions on the distant system, leading to a violation of either complementarity or no-signaling. A recent resolution shows that the paradox is avoided when quantizing gravitational radiation and including quantum fluctuations of the gravitational field. Here I will show that the paradox in question can also be resolved without considering gravitational radiation, relying only on the Planck length as a limit on spatial resolution. Therefore, in contrast to conclusions previously drawn, we find that the necessity for a quantum field theory of gravity does not follow from so far considered Gedanken experiments of this type. In addition, I will present a setup where quantization is also not sufficient to resolve the paradox. This highlights that no Gedanken experiment to date compels a quantum field theory of gravity, in contrast to the electromagnetic case.