I hate that phrase. Gets my eye all a-twitchin'.
The reason is that unique means the only one or without its like or equal.
Therefore, unique is not something that can be compared by degrees, unlike like how warm, old, or bright something is. Those words can have very added to them and make sense. Something can be more (or less) warm, old, or bright.
Then you have words like unique that are absolute modifiers. That means the word, by definition, is not something that varies by degrees. It either is or it isn't.
It's absolute. (Hence: absolute modifier.)
So you can't be slightly dead. You're either dead or you're alive.
(We aren't going into the technicalities of medicine and life support and all that . . . you know what I mean. And of course there's Miracle Max, but that's a different story.)
You could argue whether some words are absolute modifiers, like Jerry and George do in an episode of Seinfeld with dry. Jerry insists you can't over-dry something, just like you can't over-die. So he says something is either wet or it's dry. (But, you could argue, there's the in-between stage. Where does damp fit in?)
Here's a list of some other absolute modifiers (words you do NOT add very or other comparing words to):
Add "very" to any of those, and you'll see that they don't make sense.
You cannot have a "very fatal" collision. (If you mean several people died, that's something else.)
A final exam must be the last one. (You can't have one exam that's more final than another. The first one wouldn't be final.)
While trying a case in court, a lawyer wouldn't say that the defendant's DNA was very identical to the one at the crime scene.
Those absolute modifiers are a bit more obvious than unique or original. You're less likely to accidentally use one of those.
Now that you know the concept, apply it where it's most easily forgotten: something either is or is not unique.
Don't add very.