I'm sure this is bogus. First of all, this is what Amelia looked like more or less from behind. Her hair is cut much shorter than the woman in the photo, and this pic was taken right before she left:
Secondly, the Japanese-killed-Amelia line argues for a Japanese hostility towards America that was bordering on ISIS evil. In fact, Japan was not particularly hostile to America, and until FDR's oil embargo on them, they constantly pursued ways to ingratiate themselves with the U.S.
From the standpoint of the Japanese Foreign Minister (remember, in 1937, Tojo was still years away from being Prime Minister), they would have loved nothing better than to rescue her and become heroes in America. This would soften American criticism of their "intervention" in China and play into the hands of the isolationists. Rescuing Amelia would have done more for Japan by far than any sort of anti-spying vendetta they may have had.
If Amelia had spied on Japanese outposts, either intentionally or by accident, all she would have seen was Japan pouring concrete bunkers and fortifying these islands, which Japan had captured from Germany in WWI. But this was a 25 year process and was no secret in the U.S.
The bottom line is that the Japanese did not develop a fever-pitch hate of westerners or anything that would have provoked them to risk murdering someone famous until WWII actually commenced.