Sorry! You are the clerk. Honestly I am not sure about the legal position but in practical terms it would seem a bit pedantic if the public were expressly forbidden from using the services of the clerk in this way. You could perhaps discuss informally with the chair before adding such an item to the agenda. In any event, the council can always resolve no action on the item and therefore effectively extinguish any item not considered to merit thorough discussion.
With regard to matters raised in public question time you are quite correct. How these are dealt with is a matter for individual councils and their chairs. Personally I favour not giving a response unless all that is required is a straightforward reply based on agreed council policy. Certain matters must not be discussed or determined (especially matters with a financial consequence - public notice must have been given, matters requiring a decision - other members of the public might wish to make reps. but were unaware that the matter concerned was up for debate, etc.) Furthermore, depending on the nature of the matter raised a written replt affords time to give a measured reply