Manufacturers word it like this, so that consumer can basically do a risk assessment on the product. If there are no nuts used on site, then the risk of contamination is greatly reduced compared to if the site also manufactueres nut based products. Raw materials coming on site would be checked for nuts contents and as much controls put is place in possible, when bringing onto a nut free site, however it may be that they cannot completely guarentee all raw materials - the storgae in a container previously storing nuts. - the contamination risk although low, will be at the consumers descrection whether they want to risk eating it if they have a nut allergy. - unfortunalty it is all about covering the backs of the manufactuers as Mrs Overall states.
On the other nore that Mrs Overall states, on backs of peanuts it states that they may contain nuts are a peanut is not a nut but a legume and therefore you can be allergic to nuts and be able to eat peanuts and vice a versa.