Nothing speaks against that coincidence, but the brine would not be in a chemical equilibrium with the redbeds. It should reduce and bleach the flow channels. Compare the descriptions of the Kupferschiefer in Germany and Poland.
It is exactly that I observed, an hematite bleaching along flow channel in my Pyrenean outcrop.
In Mc Caig et al. 2000 papers, I read that "The brine could have been derived from the Upper Triassic evaporate and stored in the lower Triassic redbeds. Some of this formation water could have been stored in a second host-rock: in the Devonian basement or in the Silurian graphitic slates".
So, if I well understand you, the brine canot be in equilibrium with redbed, so can you think its origin could be formation water as suggested by McCaig ?
I will search Kupferschiefer papers, if you have some references it would help me.