It wasn't in the original -- at least not as more than a passing comment. I don't recall it, at any rate.
GMAOA was a weird entry in the series. It's a 2001 sequel to the 1954 Godzilla (ignores all other Godzilla movies in between) and the new take on Godzilla's origin didn't go over real well, although I rather liked it.
In Godzilla vs. King Ghidorah (1991), Godzilla's origin was given as being a Tyrannasaurus Rex which had improbably survived on a Pacific Island until WWII, when it died defending a brave Japanese platoon against the American aggressors -- died or was injured, or something, it's a long story, alternate timelines get involved. Radiation then revived the T Rex as Godzilla.
In the original timeline, Godzilla maintained some good feelings toward Japan for some unexplained reason, but aliens altered the timeline, with the result as one character says, "Godzilla is no longer a friend to Japan." Also the second-timeline Godzilla was much bigger.