I mean, it's necessary to make this work somehow to get the plot moving.
But I too cannot think of anyone who would let a thief, let alone a scheming thief who's already demonstrated a penchant for duplicity, into the kitchen under these circumstances.
The author could have sold either the "I'll try anything now" angle or the "convenient scapegoat" angles if they'd tried and added some more extenuating circumstances, but half-heartedly going for both at the same time is asking us to be pretty credulous.