Varnish is pretty awesome, but gets complicated when you have user-specific content. You can use things like edge-side includes and such, but it becomes more than plug and play at that point.
For a lot of sites, either using ESIs or including dynamic content via AJAX is a fairly simple solution that still leaves you with the benefits of caching.
For light page customizability like Hello Username. I will include the username in a browser cookie and use some JavaScript to insert it into the page. This way I can still use Varnish to serve most pages.
I believe he is saying it becomes less plug and play. By saying "it becomes more than plug and play at that point," he means it becomes more effort than plug and play.
That's my read on it, anyway. It always gets dicey interpreting the intent of others :)