But this is more advice in the style of an STD prevention campaign. "You aren't just sleeping with that gem, you're sleeping with every gem that gem ever slept with." Which, admittedly the blog author isn't taking quite to abstinence advocacy levels, but also rings kind of true.
Reimplementing basic stuff across projects probably also keeps up your programming chops. The practice would help make the trivial stuff truly trivial for you.
But what worries me about this advice is that there are some things that feel like they're trivial to implement but actually have quite a few subtleties and gotchas. In a language as dynamic as Ruby, you might even end up doing something awful (like letting your xml parser run arbitrary code). If the subtle bugs are located in gems, you only need to fix the gem to fix it all.
But then again, how often do you own the gem? Even it's open source and you can fork it, the whole point of a gem is encapsulation. You shouldn't have to be thinking about its inner workings. Some gems really can carry big risks with them.
I don't feel like I have answers to these questions right now. Just worth thinking about.