I'm not sure that's true...I've seen dogs that were quite clearly embarrassed over some faux pas they committed, and I suspect that they were blushing....but you just can't see it, that's all! Can you see a really dark-skinned person blush? I don't think you can...but you still realize they are blushing from their facial expressions, etc...

It's simply a rush of blood to the head area, caused by an emotional surge and an accelerated heartbeat...and I bet that's common to many species.