There are several issues that come to mind.
Arguably, by asking for evidence AFTER the decision, the LA is tacitly accepting that there was insufficient evidence to make a decision in the first place.
However, given that a decision HAS been made, it could be seen as implied that the LA has in fact accepted there was in fact sufficient information and evidence on which to make a decision. And, there is nothing unlawful in accepting the word of the clmt (by way of the answers on the claim form).
Given that the clmt (apparently) has stated the non-dep is a student, a higher deduction would only be justified if:
1) there was a doubt as to whether the non-dep is a FULL-TIME student (what is the wording on the claim form?); and/or
2) you are not satisfied that the non-dep isn’t working 16+ hrs etc; and/or
3) an inference has been (reasonably) drawn.
If the wording on the claim form is ambiguous, any subsequently identified o/p *may* be official error (e.g. if it is found that the non-dep is only a p-t student) . However, if the claim form is reasonably clear (i.e. the wording relates to [u:400abc2cb9]full-time[/u:400abc2cb9] student), any o/p will not normally be attributable to official error as the LA was entitled to rely on the answer(s) given on the claim form by the clmt.
Hope this helps.