Augustus
You are correct in thinking the PIP is not liable to tax.
PIP should be treated in the same way as DLA, so it might be worth asking the same again but with DLA instead of PIP.
Each Local Authority has set it's own policy in regard to Council Tax reductions, some are offering a full discount some a partial one and I am sure I read on another forum of someone complaining about their LA not offering any discount.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems