  We show that an interaction between a harmonic oscillator and a two-level
test mass (TLTM) mediated by an LOCC channel produces a signature that in [D.
Carney et al., PRX Quantum 2, 030330 (2021)] is claimed to be exclusively
reserved for channels that can transmit quantum information. We provide an
explicit example based on a measurement-and-feedback channel, explain where the
proof of Carney et al. fails, discuss to what degree setups of this type can
test the nature of the gravitational interaction and remark on some fundamental
implications that an LOCC model of gravity may have in black hole physics.
