Since you admit that my answer is correct british english then you should accept it as well as around town. Other DL courses accept both US and British variants so be a bit flexible. As I have said in other posts I am doing this course to improve my Swedish not to learn US English
“Around town” is not ambiguous in US English, or at least page after page of Google hits most being US all define it contextually as IN town. I’ve never heard it used for around a town/city either. It must be a minor usage/meaning.
“Round town” is definitely a common usage however.