3dextra,
Why don't you become the local expert? Collect all the data about grass strips, and present it to the council.
Ring the council and ask to speak to the person in charge of insurance and get the documentation regarding their legal worries. Deal in facts, not hearsay.
The only way to 'beat' them is to do the leg work and give them a solution. The council would prefer to take the easy route and stop grass strip ops because they don't have a vested interest in it.
Take it on yourself and give the council the answer you want.