Yes true.

B Corps allow the board to weigh things besides shareholder value. That's a meaningful distinction.

The idea is that shareholder primacy isn't compatible with everything every corporation wants to do, so having a board that's protected from lawsuits when they put things above shareholders is a useful thing and B Corps offer that.

The board can, for example, reject a "superior" takeover bid without fear of lawsuits from shareholders pissed off they didn't get the biggest payday available. A typical C Corp's board MUST take the highest offer, and not doing so WILL get them sued. That means if GoodGuy B Corp is about to be taken over by BadGuy Inc., the GoodGuy board can say "No, they're not compatible with the public benefit mission we incorporated under so we're not going to accept their offer." That's actually really useful.