IMHO, this is urban legend with a small bit of truth behind it.
Here is the thread from last Friday:
Passive/active DI question | TalkBass.com
Some passive basses benefit significantly from an active DI, but many (most) are fine with a decent passive DI.
An active DI should work fine for most basses, but it's not required for most.
DIs have different qualities, so you can choose different DI's based on your bass and tone goals.
For example, the CountryMan Type 85 has 10Meg input impedance and the Radial J48 has 220K input impedance. Many consider 10Meg the gold standard for piezo pickups and 220K the gold standard for magnetic picks.
One of my comments from the other thread:
An active pedal serves as a buffer for your signal. The pedal drives the DI and isolates the bass's pickups so the DI cannot load them down.
A true bypass pedal only buffers your signal when it is turned on.