Why does the coderef point to the old block?

That's not a code reference, it's a scalar reference.
$string_ref is a reference to the scalar, $string. Doing a print $$string_ref; will print out whatever's *presently* in $string.

Update: Oops ... looking at Freezy's post in the context of the entire thread, I think I might've missed the point somewhat in my reply.

Cheers,
Rob