The idea of lineage is attached to the idea of standards. In theory, if you trained with a good teacher you learned good stuff and he held you to a high standard.

If you have a purple belt from a legit BJJ instructor, chances are you've got skills. Though, like all other things, this is beginning to change..... In fact, it used to be that "blue belt" was like an old "black belt", ie that you had done about 2 plus years and had the basics down and were proficient. Now, there are a lot of "schemes" that mean blue belt is often less than it was in the past.

Ultimately, it is the person. Or, as Royce Gracie says, the belt only covers 2 inches of your butt, you've got to cover the rest