My experience with car rental companies generally speaking is that I have never been asked for the paper part outside the UK but I have occasionally been asked to show it at some UK stations.
AFAIK, all car rental companies in the UK officially require it in their T&Cs even though they do not always enforce it in practice.
On the wording, yes careless. Sixt has German origins and, like many continental Europeans, tend to use the term England/English as a generic term where those more familiar with the British Isles would be more specific and accurate, distinguishing between UK, GB and England (among others) as appropriate.