A theory $T$ is said to have the witness property if for every formula $A(x)$, if $T$ proves $(\exists x) A(x)$ then there is a term $t$ such that $T$ proves $A(t)$. The witness property is one of the criteria that are used to tell, qualitatively, whether a theory is constructive.
The definition of being a scapegoat theory is stronger than this: it requires the implication $(\exists x)A(x) \Rightarrow A(t)$ to be provable in the theory. In particular, every scapegoat theory has the witness property.
Fact: PA does not have the witness property.
To prove this, use the same sentence $A(x)$ that Apostolos gave, which says "if there is any coded proof of 0=1 then $x$ is a code for such a proof". PA proves $(\exists x)A(x)$. However, there is no single term $t$ such that PA can prove "if there is any coded proof of 0=1 then $t$ is such a code". In models where there is such a code, it will never be represented by a term.