Jeremy didn't even use Sheila as an alibi because once he told police of her illness,he could easily have said that this gun business had happened before but luckily without the same results as did happen. He could really have gone to town on that subject even by talking to Freddie and gathering a bit more info,but he didn't use anything or anybody. He didn't need to do if he was telling the truth.
Police aren't used to the truth,even amongst their own !