While McConnell's argument sounds logical, the crucial point here is how capable and well-trained are the new staff thrown at the troubled, late project? If they are capable and familiar with the domain, fair enough.
I think the fallacy here is to assume that anyone working on the project needs to be an as top-notch programmer as you are. Usually, that's not the case. Many projects only need "expert" knowledge for a fraction of the project, but the rest is just "grunt" work. There's often the odd webpage, conversion script, monitor, cronjob wrapper, test suite, documentation, etc, that can be offloaded to a "lesser" programmer, freeing up "expert" time. If only all they do is fetch coffee, or read Perlmonks for you.
A common hiring mistake I've seen over the years is for a non-technical manager to hire developers without asking developers to be involved in the hiring process and without asking candidates to write any code.
Has that actually worked for you on a structural bases? Is it worth the time it takes? (Cause not only does the developer-to-be write the code, you need people to judge it). How do you deal with the fact many candidates are under stress? Are you giving them new, non-trivial tasks, or do you give them (part of your) existing code base, and ask to modify it - the latter is for many companies a far more realistic scenario.