Adding man power to a late software project makes it later
I am living proof that Brook's law not always prevails. No, it's not because I'm extremely good in what I do (<joke>which I am, of course, cough, cough</joke>), it's just that Brook's law doesn't account for every possible scenario.
In this case, I was called to the rescue to perform a task that the main team could do anyway, but that could also be done by an outsider (thus saving precious time to that team), because it was a self-contained task for which no deep knowledge of the project was required. I simply (yeah, simply, I'll tell you about "simply") had to migrate a database, which proved to be a real PITA, but was doable anyway.
The project was late when I got there and was still late after I left, and the day after they told me the migration would have to be done again with some different specs over the destiny database (another PITA), but my point remains: the project was late, I was there, I finished my task, and I didn't delay the project further.
Hence, Brook's law not always holds.