Harrison is Robert April who found out a way to reverse-age himself.
One would think in the 23rd century, there would be facial recognition algorithms that could be run when trying to identify someone.
Pike: "This is the person we saw near the library in London."
Kirk: "Who is it?"
Pike: "The best match Picasa ... er... computer gives is Capt Robert April, but 20 years younger than he should now be."
Kirk: "Huh. Didn't he disappear 20 years ago? Maybe he found some kind of 'fountain of youth.' What was his beef? And where'd his old Enterprise go? Anyway, let's take him out!"
Or even more to the point:
Pike: "This is the person we saw near the library in London. The genetic sniffers identified exhaled DNA as being that of Capt. Robert April, so we don't understand why he'd change his appearance if we had this level of technology to fingerprint people..."
Apply this thinking to 99% of Trek and you see holes in everything :P Trek is still sticking to its 60s blueprints atm and none of this stuff was even dreamed of back then