There’s a difference between brine and granular salt applications
You apply brine when it is expected to freeze and get snow. The brine keeps it from sticking hard to the road surface. But it can’t be placed if it is going to rain as you pointed out because it will simply wash away.
Some agencies still use a salt/sand mixture which can provide some breakup and better traction.
For extreme storms on the mountain passes Washington DOT uses a product called Ice Slicer and it will melt away the compacted snow and ice really fast.
I've used regular rock salt, but it terribly spalls our concrete driveway. A couple years ago, I bought magnesium chloride but the damn stuff liquifies during the summer months and leaks out of the bag making one heck of a mess.
Yep, sand/salt mix is the normal follow-up here after the snow falls. I haven’t heard anything about why it wasn’t done. I have heard reports of plows and spreaders sitting idle, possibly waiting for taskings and not getting them.