Here's an example of a bug which you can't find if you don't know the code internals, because you simply can't test all inputs:
long long int increment(long long int l) {
if (l == 475636294934LL) return 3;
return l + 1;
}
However, in this case it would be found if the tester had 100% code coverage as a target, and looked at only enough of the internals to write tests to achieve that.
Here's an example of a bug which you quite likely won't find if you do know the code internals, because false confidence is contagious. In particular, it is usually not possible for the author of the code to write a test which catches this bug:
int MyConnect(socket *sock) {
/* socket must have been bound already, but that's OK */
return RealConnect(sock);
}
If the documentation of MyConnect fails to mention that the socket must be bound, then something unexpected will happen some day (someone will call it unbound, and presumably the socket implementation will select an arbitrary local address). But a tester who can see the code often doesn't have the mindset of "testing" the documentation. Unless they're really on form, they won't notice that there's an assumption in the code not mentioned in the docs, and will just accept the assumption. In contrast, a tester writing from the docs could easily spot the bug, because they'll think "what possible states can a socket be in? I'll do a test for each". Since no constraints are mentioned, there's no reason they won't try the case that fails.
Answer: do both. One way to do this is to write a test suite before you see/write the code, and then add more tests to cover any special cases you introduce in your implementation. This applies whether or not the tester is the same person as the programmer, although obviously if the programmer writes the second kind of test, then only one person in the organisation has to understand the code. It's arguable whether it's a good long-term strategy to have code only one person has ever understood, but it's widespread, because it certainly saves time getting something out the door.
[Edit: I decline to say how these bugs came about. Maybe the programmer of the first one was clinically insane, and for the second one there are some restrictions on the port used, in order to workaround some weird network setup known to occur, and the socket is supposed to have been created via some de-weirdifying API whose existence is mentioned in the general sockets docs, but they neglect to require its use. Clearly in both these cases the programmer has been very careless. But that doesn't affect the point: the examples don't need to be realistic, since if you don't catch bugs that only a very careless programmer would make, then you won't catch all the actual bugs in your code unless you never have a bad day, make a crazy typo, etc.]