It's certainly a difficult question and every attempt I've seen at defining the role of a councillor over many years working within the sector has not been universally accepted. In some respects, I believe the Good Councillor Guide was an attempt at defining the role but that in itself has often been held as being inappropriate simply because it was drafted by the National Association of Local Councils, deemed by some as some kind of unauthorised rogue organisation. Our sector is governed by out of date legislation which is open to interpretation but I also question whether anything more defined would be effective either. It is a fundamental element of democracy that anyone can stand as a local councillor (subject to criteria generally based on links to the area) yet that in itself can mean that the reason why people put themselves forward can be open to abuse by those whose personal objectives might be less than honourable.
I have concerns with the quote you've highlighted as it clearly shows that the chair of that council appears to be taking decisions that a single councillor, whether chair or not, is not empowered to make. Within our communications policy it is stated that councillors are encouraged to engage with the community but each must remember that they cannot state that they act on behalf of the council in any matter unless they have been clearly authorised to do so by full council. It seems to work for us but we all work pretty well together. Not sure it would work with all councils.