To Williams it was a win-win as 'they' had their man and and he didn't have to deal with the sixth floor....so he thought.
Seems he only thought that for a short period. His story starts to "evolve" on the Saturday with a mention of a brief trip to the 6th floor around "noon". The chicken lunch is not admitted to by him until the 25th to Lt Day. Nothing in any official documentation about his chicken lunch until Dec 2.
At his first statement around 2pm on the Friday, consider what he knew? He knew the shots came from above, maybe just where he had been. He had left his unfinished lunch there. Maybe someone had seen him (Rowland!). He knows the 6th floor is of interest as that is the reason Fritz ordered Stenkel to round up those workers on the 6th floor that day for questioning. He knows he has an alibi for the time of the shooting (Jarman and Norman). He likely does not know of the Dillard photo at this early stage. He knows Oswald is of particular interest and is questioned about him. he knows Oswald has been arrested and is in custody. At this stage the cops do not know if Oswald did any shooting at the TSBD, maybe he had co-conspirators who he assisted In the plot.
The chicken lunch is being referred to as the assassin's lunch by that afternoon all over the media.
Does anyone think if Williams noticed Oswald on the 6th floor any time after the elevator race that day he would not ever mention it to the cops? Interesting comparison to Givens.