Okay stick with me, cause this is going to be a bit complicated.

So we've been learning about genetic profiling in my genetics class. Basically, it's how scientists can tell where a blood/saliva/literally any DNA sample came from if they have a comparison. It can be a minuscule amount or really old, whatever. Science, right?

But anyway, Matt tends to bleed all over Hell's Kitchen. And maybe no one is trying to figure out who Daredevil is after the whole taking down Fisk thing, and maybe it's an accident. But for some reason, some of Matt's DNA gets picked up and it's sitting in a database somewhere.
If he was ever accused of anything and forced to give a DNA sample, it would be a match. And sure, he could explain one blood sample away, but his DNA is literally scattered over the city. That's a bit harder to explain.

Now, this is where Matt's twin comes in. Because the science isn't sequencing the entire sequence of DNA, it's just looking at parts that are individual to everyone. If you look at enough parts, the odds are so high that there aren't enough people in the world for there to be another person with the same markers.
Except for identical twins.

Now, maybe Matt knows this, maybe he learns shortly after Brett pulls him aside and asks him before the rest of the shit hits the fan, what exactly his blood is doing everywhere.

So Matt invents Mike. It's not actually a terrible plan, because here's someone he can blame the DNA on. And of course he can act sighted enough for Mike to be sighted, unless people start flashing lights around or using screens. (It's not a perfect plan.)
So once that is cleared up, Matt is in the clear, and Mike can skip town. Problem solved.
(Except Foggy is dying with laughter and the whole thing is just a mess, but it worked, right?)

+ maybe Matt can claim that when his mother left, she took a twin with her, and he didn't know until he was a teenager or something. Foggy's just sitting there nodding like 'yeah I met Mike during college. He's a wild guy.'