Uh no, if that was the case, then the vast, vast, majority of casualties would be recorded as MIA.
That was the case.
Not vast majority, but very large part of casualties are indeed recorded as MIA immediately after the battle / campaign. Only later the number of MIA is being verified (usually downwards), as it turns out that various people who previously were recorded as MIA, are found out to be dead or alive (e.g. in enemy captivity).
MIA basically is everyone who is not confirmed killed or confirmed wounded, but is missing from his unit.
To be honest, a lot of books and records now do combine the KIA/MIA columns
When these books / records are compiled a very long time after the end of a particular battle / campaign - then indeed they do. But by that time, majority of MIA are already verified to be KIA. Also when you are recorded as MIA for many years, you can be judged dead and moved to KIA column.
However, immediately or short time after the battle / campaign is over, MIA and KIA columns are not combined.
For example in daily reports or weekly reports. Or even in summary reports compiled shortly after the end of a campaign.
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Germans during WW2 had a special Commission the task of which was to research the cases of MIA soldiers. The longer time from a particular wartime operation had passed, the smaller was the number of MIA and the higher the number of KIA (since MIAs were gradually being moved to KIA column).
A report compiled 10 days after the end of the 1940 Westfeldzug is going to show different numbers of KIA & MIA, than a report compiled 3 years later.
Same with other campaigns. For example a casualty report by Wehrmachtverlustvesen dated 30.11.1944 (it compiles casualties from various campaigns up to this point) says that casualties of the German Army (Heer - ground forces - this does not include casualties of Luftwaffe and Kriegsmarine) in the Polenfeldzug of September 1939 amounted to 16843 KIA and 320 MIA (total 17163 KIA and MIA). If you compare this to any earlier report, you will see that the number of MIA was much higher there. For example shortly after the end of the campaign (so when all POWs captured by the Polish army were already recaptured by the Germans - thus could not be included among those MIA) the number of MIA was reported between ca. 3,500 and ca. 5,500 (depending on date of the report).
This means that immediately after combats, only soldiers who undoubtedly were killed, are reported as KIA.
Others are reported as MIA and then gradually their deaths are being verified.
So I am sure that your father was reported as MIA for one month. The probablity that they reported him as KIA without having a body is small.
Unless, of course, procedures leading to recognizing a soldier as KIA were less strict in the US Army than in the German Army.
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And such a curiosity:
Even nowadays Japanese casualties on Iwo Jima officially include 12,000 MIA. They were never 100% confirmed as dead:
http://www.guardian.co.uk/world/2011/feb/15/japanese-prime-minister-iwo-jima
Bodies not found = soldiers are missing, not KIA (even though we have year 2013 and the battle was in 1945)...