There is a basic fallacy in the beginning of this article, factually incorrect: An active instrument MAY be able to be directly plugged into a line input, but most cannot - their output is too low in level for a clean recording (or live amplification). They need a DI into a mic input for best sound. That said, the general rule is, active instruments (usually defined by having a battery on board) can use a passive (transformer only) DI box, and a passive intrument usually likes to have an active (phantom powered) DI.
But even that is only a general rule. I usually use active DIs most of the time, except on keyboards which have more robust output stages. But even there, an active DI will work fine if that is what you have!
Lou Judson, professional live and recording engineer.