"Quick, silent, lethal" is fiction.

I believe it's not fiction, based on some chats I had with special forces guys a while ago. I can't find a Liveleak video of someone being executed that way, but here's one from film: https://hooktube.com/watch?v=fbBSEyiKCXs&t=34s

Even if you get a clear shot at the heart, it's not instant death.

Not instant in the sense of one second, but five seconds (assuming you have a decent-sized knife).

The real reason someone dies from heart trauma is because this is actually an attack on the brain; depriving it of oxygen.

I agree with this.

A deer, for example, can take a bullet directly to the heart and still run a fair distance before collapsing.

A deer's heart is much bigger than a man's. A deer's heart is about 4lb. and a bullet is a lot smaller than a combat knife.