I think the quote is about the fallibility of the humans who convert theorems into statements of type theory. You could end up with a valid theorem, but not the theorem you meant to prove. This would be a bug in the statement of the theorem, not the proof.
For example, you might want to prove that a certain sorting algorithm is correct. You formalize the specification as "for every two integers i, j, output[i] <= output[j]" and prove that outputs of the algorithm satisfy this spec. However, this is not a correct characterization of sorting, since the algorithm might return the empty list.
For example, you might want to prove that a certain sorting algorithm is correct. You formalize the specification as "for every two integers i, j, output[i] <= output[j]" and prove that outputs of the algorithm satisfy this spec. However, this is not a correct characterization of sorting, since the algorithm might return the empty list.