Seems a little vague really, whilst they can't "charge you for collection of household waste", it's pretty obvious that a part of your council tax goes towards funding that. With no mention in the rules about frequency, that can give the council powers to stretch it. For some time many councils have been discussing/looking at reducing frequency so general waste is only picked up every 3-4 weeks.
The argument about bins smelling should be moot because things like food waste should go in a separate bin that should be collected more frequently. Our council has skinny wheelie bins for general waste, and although there's only 2 of us and a dog, we probably only fill the general waste bin to maybe 60-70% a fortnight. So we could do a stretch to 3 weeks without too many problems. If there was a proposal to stretch it to monthly pickups, then they'd need to be providing bigger bins.