There's a difference between code tests though and spec verification.

Spec verification is (should be...) black-box integration testing. And yes, this is a good chance to get a second set of eyes on the spec to make sure nothing was missed in the implementation. (unit-tests can't catch missing code!)

Code tests should be more white-box and should be measured against line/code coverage instead of spec coverage. These are what I think the original devs should write, and should be 95%+ of the total test volume.

The problem with expecting testing to pick up spec errors is that it takes comes at the end of the design/build phase instead of the beginning when you can make changes easily.