The first example in the synopsis uses $_, I added a comment to make it more explicit. It's also mentioned in the XML::Twig 101 section.
I know that the docs are a bit overwhelming and hard to read.
The main reason is probably that XML::Twig it's too big. This comes from a decision I made, a long time ago, to have just 1 massive module, instead of several ones. The reason at the time was to allow users to install the module easily, especially on Windows, by simply copying Twig.pm in the proper place. At the time there were no Strawberry Perl, perlbrew or local::lib... If I were to start again I would certainly break up the module in several sub-modules (as with XML::Twig::XPath).