Was he claiming income based JSA (JSA IB) or contribution based JSA (JSA CB)? The
DMGs that you refer to are meant for DWP staff and the Home office has slightly different standards.
A jobseeker of more than six months needs to prove not only that he was seeking work, but also that he had a "genuine prospect of finding work".
Be aware that since November 2015, EEA citizens must apply for a DCPR before applying for naturalisation.
I am not a lawyer or immigration advisor. My statements/comments do not constitute legal advice. E&OE. Please do not PM me for advice.