It is not a myth.
If you have made the pavement more dangerous and someone breaks a leg, morally and legally why shouldn't you have to contribute if the council are sued?

Shovelling compacted snow away makes the pavement neater and sparkly and you'll feel good in a Dr Suess 'All this snow has to go" sort of way, but you are often exposing an icy layer that is more dangerous than before.

The best thing for levels of snow fall measured in inches rather than feet imo, is just to sprinkle rocksalt on top of the snow on the pavement - it improves grip, helps break up the compacted snow/ice and melts the stuff quickly once it has warmed a little.

It takes 5mins to do and is cheep as chips. But the council need to provide it - it is their pavement at the end of the day.