The reason Pinterest verification doesn't work with Jetpack is that Jetpack asks for the full Pinterest verification tag. In fact you only need to enter the code number, not the surrounding html.
So that's what this plugin does, it just asks you for the code number and generates the meta tag. It's what Jetpack should do.
You may as well use it - but if you fill in the Jetpack field as well, you'll end up with two identical tags which could cause problems. Just so you know.