To be fair lets just say that under stress of battle, and without much prior firsthand knowledge and visual familiarity with enemy aircraft beyond sighting guides, that after action reports can be at best confused, sometimes unreliable, and other times down right wrong.

We obviously know this to be a case of seeing something that wasn't there now, but also the Allies tended to greatly exaggerate the amount of inter Axis cooperation hat went on, in part if we are being generous because they were projecting about their own level of cooperation.

In addition to this sighting there were numerous other reports of ME-109's through the first year of the war in the Pacific. A few popped up everywhere from the Doolittle Raid, to Coral Sea, and Midway. And while a handful of copies were sent to Japan for examination there was little mutual development and those aircraft were not used in battle. What did happen though was the transfer of engines for license production.

So Japan did construct two aircraft that could be sources of confusion. The first is the Ki-61 "Tony" which was called that because it was designed around an Italian engine. It did see much service in the South Pacific from 1942 on, and even did defend Tokyo during the Doolittle Raid(and hence was the source of that sighting we can say). However save for the fact that it was the rare Japanese water cooled engine design it bare little similarity to the 109..

The other option then was the D4Y "Judy" dive bomber built to be the replacement to the Val. It was powered then by a license copy of the Daimler Benz engine from the ME-109 itself, and a prototype recon variant was actually present at Midway. While not perfect again it is understandable that unfamiliar and stressed out pilots might see something that isn't actually there based on it.

We can also examine the context of the memo itself. Since it was clearly written day of, likely by Kimmel's Pacific Fleet staff who were essentially collectively in shock at that point. You will notice that it is in general very patchy and rough in its info. Such as why mention Oklahoma and not Arizona. Or why Tennessee and not West Virginia or Nevada.

FDR was recieveing information about the scale of the attack in drips and drabs. He spent the day in his study on the 2nd floor of the White House while his subordinates including SECNAV Knox, and CINCUS Admiral Stark. While his secretaries rotated through sitting on the phone first in the room then squeezed out and for better hearing to a bedroom next door. They would receive intermittent calls from members of Stark's staff in Hawaii who with each call were more and more despondent and spreading a general sense of gloom. Then each new update was typed into a memo like this and taken to the President whose mood was deteriorating with each update imagining all those proud ships and men he loved so dearly decimated.

Here is the relevant part of the memo http://imgur.com/iGjSW5X