The only way I could see this being an issue is if you're using canonically-different links to get to the same page. If you have one link that goes to "/", and another that goes to "/default" or "/index.htm" or whatever your homepage happens to be. When Google's spider crawls the site, it will try each link, and start to discard duplicate-content at the end of links, so you can end up with some SEO fragmentation.
But if all your home-links point to the same URL, that shouldn't be an issue.
A lot of FUD gets thrown around in the SEO-sphere. As initall said, "Home" might be a waste of a keyword, but the most important aspect in SEO is content, so try to direct your client's attention to building their authority through solid content that draws a lot of people to link to them organically, and that will serve them far more in the long run than debating the potential impact of a "home" link.