At the time, nobody outside of Japan new it happened.
When Backlund tours Japan, if I'm not mistaken, he loses the title on the first night. On the final night of the tour, Inoki retains by DQ but refuses to accept the belt that way, which results in him "vacating" the title in front of the Japanese media. Backlund returns to the states, still champion, but because the MSG show was going to air in Japan, a match was held to crown a new champion, which Backlund. However, he was only the new champion to the Japanese media, while in America, the victory was seen as a successful title defense since nobody here knew he lost the title to begin with.
Now, the reason Inoki won the title to begin with had to do with his war with Giant Baba. This was done as a way not only to get one up on Baba (who just lost the NWA Title a few weeks prior) but also build up Inoki's status. It all goes back to the rivalry between Baba & Inoki, with certain people not wanting to work for the other out of loyalty and the "anything you can do, I can do better" level of undermining that was going on at the time to prove who was number one.
As for the second question, that's been the case with Ric Flair quite often. Goes on an overseas tour, loses the title the first night, gets it back at the end of the tour and nobody in America is even aware. In those days, I'd imagine that was quite common with all major touring championships. You never had to come up with an explanation behind it because, 35-40 years, they didn't expect this much information to be out there and kind of make a situation seem weird.