HBR 86 (+ CTB & PC-age equivalents), HBR 83, DAR 13 and DAR 20 contain the legislation for requesting evidence and information. There are also provisions in the FtT Rules. Each has a purpose dependant on the stage of the administration process.
The DWP’s grasp of the LAW has been stunningly tenous for as long as I can remember. Ignore what the DWP says.
In principle, there is nothing in law preventing a LA from accepting only the information on a claim form along with a claimant’s verbal statement about his/her circumstances. However, LAs have the power to ask for evidence / information that is “reasonably required” (this phrase being used in HBR 86).
The rule of thumb is this: Is is sensible to ask for evidence? If so, it will be reasonable to do so in 99.9% of cases.
Does the legislation mean different LAs will take different approaches? Yes. Should the law allow such inconsistency? From a professional / practioner perspective, that latter question is irrelevant – it’s a matter for the government.