Ask an average the Americans what happened then and you'll hear all sorts of fantastic versions, if not "umm I dunno".
Absolutely true -- a well-educated American of Peter's age would most likely recognize "7 December, 1941" as the day that Pearl Harbor was bombed (everyone's heard sound-clips of FDR's "a day that will live in infamy" speech!). But "22 June, 1941" would have no immediate significance for him. He might also remember that Americans landed at Normandy sometime in June 1944, and that Germany formally surrendered in May 1945, and Japan in August 1945 -- but he probably wouldn't know any specific dates of major battles between Germany and the USSR.

It might be a funny (and realistic) detail to have Peter remembering to himself "that movie I saw a few years ago about a German sniper and a Russian sniper, played by what's-his-face, Jude something... it was during the siege of Stalingrad -- or was it the siege of Leningrad? -- no, wait, Stalingrad and Leningrad were actually the same city, but they renamed it during the war -- was that right? It sounded right, he was almost 90% sure..."

Related to this: as has been pointed out, Ann seems oddly unsuspicious at finding an American in rural Belarus! Even allowing that Ann, by nature, is not a stereotypical sovok who's paranoid of foreign spies -- in fact, she's very curious and open-minded about foreigners, which is why she worked so hard to learn English -- in 1941 her first thought should've been "How do I know he's not a German?" And her second thought, perhaps: "Or how do I know he's not an NKVD agent trying to test me, to see if I'm a traitor?"

So it might be worthwhile to write a few more paragraphs of dialogue between Ann and Peter in which she is trying to figure out if he's a German, while he tries to persuade her that he's NOT German! Of course, his strange comment about "Mr. Barack Obama" would, on the one hand, cause her puzzlement, but on the other hand, would give her some reassurance that he was neither a Nazi spy nor an NKVD officer!