Quite often it is by a process of elimination when cross checking statements that the police are able to tie the pieces of an investigation together which enables some investigative progress to be made.
The PJ had been given Jane Tanner's witness statement at the earliest opportunity.
They had the creche records to hand which could have led them to any other individual such as Dr Totman legitimately out and about while carrying a child had they bothered to check at the time.
They had absolutely no chance of checking the information the Smith family held for the simple reason that they were not informed about it ... and by the time they were ... it is my opinion that the path the investigation was to take was set in tablets of stone.
Anyway, they paid scant attention to the information given to them by the three Smiths who came over to make statements on 26th May as no action was taken until after the 20th of September when Martin Smith amended his statement.
I think that if the PJ had all the information to hand regarding movement of individuals carrying a female child in Luz as close as possible to the 4th of May, it could have led to a far different outcome than the one we have been left with.