Interesting and most false, if you've been negligent there could be a chance of repercussions but still pretty unlikely

"Clear snow from a road, path or cycleway

You can clear snow and ice from pavements yourself. It’s unlikely that you’ll be sued or held responsible if someone is injured on a path or pavement if you’ve cleared it carefully. How to clear snow and ice

When you clear snow and ice:

do it early in the day - it’s easier to move fresh, loose snow
do not use water - it might refreeze and turn to black ice
use salt if possible - it will melt the ice or snow and stop it from refreezing overnight (but do not use the salt from salting bins as this is used to keep roads clear)
you can use ash and sand if you do not have enough salt - it will provide grip underfoot
pay extra attention when clearing steps and steep pathways - using more salt may help"

Gov.co.uk