First off, I very rarely (can't remember the last time) get hacked off at my partners when they call something, even if it's in front of me. I just don't take it as them trying to grandstand or show me up. I assume they saw something they felt needed to be called. We would definitely discuss it in the locker room, but there wouldn't be any anger involved. It's ridiculous to get angry about something like this - we all have brain farts every now and then, so why not just assume your partner had a brain fart and move on.
Secondly, I am not going with a blarge on this one. If the upset coach asks me, I will simply say "I don't know Coach, but here comes Snaqs. You can ask him."
Third - I'm not calling an assignor over this play. It really isn't that egregious of a mistake. No rule was set aside or misapplied. A partner called out of his primary in front of me. If I call the assignor about that, I look like a little whiner. Not needed.