There are two types of JSA. Given that your post refers to your brother-in-law nearing the end of a 6 month entitlement, I assume that he's been receiving contribution-based JSA. That's paid to people who've made a sufficient number of National Insurance contributions prior to becoming unemployed. There's no 'means test' applied and it lasts for up to 6 months.
Someone who's unemployed but not entitled to contribution-based JSA (either because they've not paid enough National Insurence or who, like your brother-in-law, has come to the end of the 6 month period) is normally eligible for income-based JSA. The full rate is exactly the same as contribution-based JSA but the entitlement is reduced if the claimant has over �6000 in savings.
You state that information on the net seems to be contradictory. I can assure you that my post is accurate because I'm currently receiving income-based JSA after coming to the end of my 6 month entitlement for contribution-based JSA. Further I can provide a link to the official DirectGov website:
http://www.direct.gov.uk/en/MoneyTaxAndBenefit s/BenefitsTaxCreditsAndOtherSupport/Employedor lookingforwork/DG_10018757
Chris