There is depression due to brain chemical imbalances, which would need medical intervention. However, PD's are not brain chemical imbalances, they are a person's personality. Depression is common for people with PD's due to their life circumstances, but it's not always present.

One way someone with a PD could avoid depression, if this video is correct, could be to express anger instead of stuffing it away. (There's also the loneliness component of AvPD, which can also cause depression, but that's another story.)

The problem is getting up the gumption to say something when someone else does you wrong. You have to feel secure and worthy to speak up, which is hard for a person with AvPD, or at the end of your rope. And if that somehow happens, then the people you're talking to have to be receptive.

So, really interesting idea I think, that depression can be more due to unexpressed anger than sadness, but that doesn't help you if you can't speak up or the people you need to speak up to aren't responsive.