That’s a new one!
The AIF exists for the purpose of calculating income and it doesn’t affect the applicable amount at all.
If you don’t include the SDP in the HB applicable amount you will be clawing back most of the advantage the claimant gained from having the SDP included in their Pension Credit.
For a person with an SDP to have an AIF, they must be in the income range where their non-AA income is just a bit higher than the standard GC rate plus the SDP. If you apply that income, plus SC, against the normal HB applicable amount, they will have a hefty contribution to make towards their rent which will leave them with less money to live on than GC including the SDP.
By awarding the SDP in HB, you ensure that they only contribute to their rent out of any income they have in excess of the GC+SDP rate.
So you were right all along