Well, the short answer is The Narrator isn’t Michael. Burn Notice used a third person omniscient narrator voiced by Jeffery Donovan (who also played Michael).
The basic reason to assume they’re not the same character is because The Narrator leads into things that the character does not know, far too frequently. And occasionally outright contradicts things Michael says.
Additionally, the narrator doesn’t leave when Michael isn’t present. This may seem like an odd thing to point out; but, let’s talk about what a narrator is for a moment.
Fundamentally, the narrator is the one telling you the story. This can be a character in the story, or it can simply be an impartial observer, relating information back. They can be honest, or not. They can inject their own editorializing, or not. They can be omniscient, meaning they know everything that is happening, and are privy to what characters are thinking, or not.
Even when your narrative is supposed to be impartial, you still have a non-personified narrator. And they need an internally consistent tone relaying the information back to the reader. As a writer, you get to make a lot of choices about how your narrator, functions, so let’s talk about some of those and how they work.
First and third person narrators are one of the most obvious cues as to who your narrator is. At a very basic level this is determined based on which set of pronouns your narrator uses.
First person suggests a narrator who is an active participant in the story. Often this is the protagonist, though that’s not, strictly, mandatory. Watson, for example, is the narrator of the Sherlock Holmes short stories, even though Holmes is the protagonist. Another example would be The Great Gatsby by F. Scott Fitzgerald, where Nick Carraway is telling the audience the story of Jay Gatsby via his own personal experiences. An example of the narrator being the protagonist is J.D. Salinger’s The Catcher in the Rye where Holden Caulfield tells the audience his story. From Twilight to The Hunger Games many novels for the Young Adult sub-genre follow this format.
Third person puts more distance between the protagonist and the reader. It’s a barrier you can use when you want the reader to empathize with a character, but don’t want to endorse their behavior. Or when you want to create a layer of detachment between your characters and the audience.
Omniscient narrators are all-knowing. They have access to, and share information without being tied to any individual character. When this is first person, you usually end up with a narrator that’s editorializing or commenting on the events portrayed.
They can still be a character in the story. This is most common with narrators who are reflecting events in hindsight. In a memoir, for example.
Which is one legitimate read of Burn Notice; An omniscient narrator, who might be a future version of Michael Weston, recounting events that happened in the past, with access to information he didn’t have at the time.
Limited narrators are a character in the story. Strictly speaking their information is restricted to what one of the characters knows. It is possible to jump between different characters to create a larger mosaic of information for the reader. George R. R. Martin has a serious fondness for this specific approach, if you’re wanting an example.
Objective narrators are dispassionate about their characters. That is to say, they don’t care how the characters feel. They’re primarily concerned about what is happening.
Subjective narrators are more interested in what a character is experiencing. What they’re feeling and thinking.
To some extent, objective and subjective narrators are a sliding scale of what you’re priorities are. If you’re more interested in what your character is going through, you skew more towards subjective. If you’re more interested in a procedural, “just the facts ma’am,” Jack Webb approach, then you’re looking at objective.
With an objective narrator, you’re under no obligation to make them a part of the piece. They can literally simply function as an exposition dispenser, filling the audience in on relevant background context. It’s an aesthetic choice, but there’s no “in universe” justification. The narrator is there to make sure the audience understands the context of the situation. Tom Clancy, back when he was still alive and not just a brand perpetuated via editorial necromancy, was excessively fond of this approach.
For the most part, this is what Burn Notice does. The Narrator exists to explain tradecraft to the audience. It’s not a part of the story. Ultimately, there is no metafiction context, of a future Michael teaching a class on espionage. It’s just there to ensure that the show is watchable, and understandable. And when you stick Burn Notice next to something like The Sandbaggers, the reasoning becomes clear. Intelligence is a very obtuse business. People act in counter intuitive ways because it is about subverting expectations, and being a step ahead of what someone’s natural reactions would be.
When you’re writing, you pick your narrative tone, to control how your story feels, and how “close” they are to the characters. First person, subjective, will stick you inside a character’s head. However, it is you placing all your eggs on your narrator being interesting enough to carry the entire narrative on their shoulders. Third Person Limited is the middle ground between the two, and may give you opportunity to open up to other characters as narrators to provide alternate viewpoints on events. Third Person Objective can be downright clinical. Picking the right one is an important part of choosing the story you want to tell.