Both approaches would be valid and I don’t know which one is better.
The advantage of the posted approach to repeat the channels is that you could just use a pretrained model (which usually works on RGB data) without any manipulations or finetuning of the first layer.
E.g. if you change the input channels of the first layer to 1, you could

use a reduction (such as calculating the mean/median/sum of all channels),
initialize this channel randomly and train it,
or keep a single channel only (which one?).

However, I haven’t run any experiments to compare these approaches.