Let's assume that Amelia didn't fly non-stop for the last 74 years. Let's say she landed to eat, sleep, re-fuel the plane, and so on. She might have been able to do this without getting recognized, if she landed in foreign countries, and/or wore a disguise, and/or used a fake name. Also, after a few decades, she would start to look different because of age, and would therefore be unrecognizable. People would only have photos of her 39-year-old self. (I'm actually surprised that the guy in the comic recognized her.) So let's assume she landed often, and she only flew 8 hours a day.
She would need money to pay for all that food, places to sleep, plane fuel, and so on. So let's assume she worked some odd jobs to earn some money. Again, she'd have to hide her identity in the ways I described above. Let's say she flew 8 hours a day for one whole year, then worked and made money for one year, then flew 8 hours a day the next year, and so on, alternating years like that. That means she would only be flying for half the years, or 37 out of the 74 years.
Let's also assume that she's one of the lucky few people in the world to survive well past 100 years old. She would be 114 years old if she were alive today. The oldest person in history, whose age is verified and undisputed, was 122 years old when she died. So Amelia surviving to 114 is not completely impossible.
That gives us 37 * 8 * 365 = 108,040 hours of flying time.
The cruising speed of a Lockheed Model 10 Electra is 306 km/h. This gives 108040 * 306 = 33,060,240 km as the distance that she would have covered.
The circumference of the Earth is 40,075 km. 33060240/40075 = 825 (rounded). So she could have circled the globe about 825 times. So even with all these assumptions, this still doesn't make sense.
I actually prefer the idea that someone else suggested, of flying at relativistic speeds and experiencing time dilation. For that, I would imagine that her plane would have to be abducted by aliens, and upgraded with alien technology that allows it to double as a spaceship, fly outside earth's atmosphere, and accelerate to something like 99% of the speed of light. Someone who's more familiar with relativity should do the calculations for that.
“The aim of argument, or of discussion, should not be victory, but progress.” - Joseph Joubert