There are many stories with the theme of "primitive" tribes and civilisations having access to knowledge only available through advanced technology they didn't possess (see note 1). Sometimes this is presented as originating from older civilisations, which were supposedly more advanced than modern anthropologists accept. Sometimes the knowledge is supposed to have come from supernatural sources: gods, angels, etc. But the most common theory is that it came from extra-terrestrial visitors. Sometimes these aliens just visited and provided the knowledge without doing much else, sometimes they are part of a creation myth or assisted with advancing the civilisation in question (see note 2).
One of the more interesting myths involves the Dogon tribe of western Africa. They have a myth, which supposedly goes back 5,000 years, where aliens from Sirius visited and gave them knowledge which wasn't available at the time because a telescope would be necessary and invention of the telescope was still thousands of years in the future (see note 3).
The knowledge included the fact that Sirius is a double star (see note 4). A small companion star orbits Sirius itself every 50 years. The companion star of Sirius is dim enough and close enough to Sirius itself that a telescope is required to see it. They also knew that the companion is a dense dwarf star, made from the "heaviest metal in the Universe". All of this is true (within the limits of the simple language used), (see note 5) so how did this primitive tribe know all this?
Other facts which should only have been known to western science included the four moons of Jupiter, the rings of Saturn, and that planets orbit in elliptical orbits. These are also approximately true (Jupiter has 4 big moons but many small ones, and other planets have ring systems but Saturn's is by far the most spectacular). They also believed there were planets with different kinds of people on them which orbit six other stars in the sky. Of course, there is no evidence to support this.
The beliefs were originally reported by French anthropologists Marcel Griaule and Germaine Dieterlen. This report was then used (or misused) by Robert Temple in his book "The Sirius Mystery". Even the original research done by Dieterlen has been criticised, especially by Dutch anthropologist W.E.A. van Beek, who spent seven years with the Dogon, and suggested that the original research relied too heavily on only one informant who may have been influenced by the teachings of a Jesuit missionary who had lived in the region prior to the anthropologists' arrival (see note 6).
Carl Sagan has suggested the findings might be based on selective evidence, and other skeptics see evidence for cultural contamination from visiting astronomers who went to the region to observe a transit of Venus. The fact that the knowledge contained the same errors and approximations which might have been common for a western visitor at the time is significant. For example, the existence of a third star in the system was widely suspected by western science at the time, and also occurs in the Dogon mythology.
Temple goes further and claims the beliefs are much older. For example, the Dogon had a ceremony called Segui which celebrated Sirius and occurred every 50 years (the same period as Sirius-B) which goes back for centuries. But an interest in Sirius is common in many cultures (see note 7) and the actual period between the ceremonies was between 40 and 60 years, so a precise relationship can't be established.
But Temple takes the debate even further. He claims links between Dogon myths and ancient Sumerian myths. If this was the case the argument for the myths being based on modern western information would be invalid. But there is no real evidence in the ancient records supporting this idea. Many other subjects are described in unambiguous language, so why should this only be mentioned in bizarre riddles which can be interpreted many ways?
So, in summary, I think the mystery is solved. The Dogons heard some new information about their favourite star (and other astronomical topics) from visiting astronomers and/or other western visitors. They assimilated it into their culture (anthropologists have found this is to be common amongst people they studied), and that's where the story started. The story was taken over by Robert Temple and embellished with some unsubstantiated pseudo-information. But in the end the explanation is simple, and elaborate theories regarding aliens are unnecessary.
Like most ancient knowledge myths, this one really isn't difficult to explain without resorting to bizarre theories which contradict mainstream scientific and historic knowledge. Therefore I give this a really high score on the crap-ometer!
1. The most famous example would probably be the theories of Erich von Daniken, from his books, such as Chariots of the Gods. He cherry picked various "evidence" for many unlikely stories, such as an alien runway in ancient Peru.
2. Erich von Daniken also invented theories which suggested the Egyptian pyramids were built with the help of advanced aliens. This is a popular theory with other writers too. Using classic fallacies, such as the argument from personal incredulity they claim the pyramids are too big and precise to have been built by the Egyptians. Of course, we know that using simple methods, and very large numbers of workers, building pyramids is possible without advanced technology.
3. The telescope was invented in 1608 by Hans Lippershey and was first used to observe the sky in 1609 by Galileo Galilei. There is some evidence that lenses were made in the 10th century and they might have had functionality similar to a telescope, but they would most likely not have been adequate for astronomical use.
4. In fact the myth mentioned two companion stars, which might be a critical error in the whole story, because at the time astronomers thought there was a third star but this later on turned out to be untrue.
5. Sirius is the brightest star in our sky (mainly because it is quite close, not because it is genuinely bright). Sirius is 8.6 light years away, and is over twice the mass of our Sun. The companion is roughly the same mass as the Sun, but only 12,000 kilometers in diameter (the Sun's diameter is about 1,400,000 kilometers). The companion star is 10,000 times fainter than Sirius, which explains why it is difficult to observe.
6. Germaine Dieterlen spent 20 years living with cultures such as the Dogon and made many important contributions to the study of myths. But her work on the astronomical knowledge of the Dogon has been criticised as being too credulous. There is an entry for her at Wikipedia.
7. Sirius is important because it is the brightest star in the sky, but it was also used my many cultures to time the seasons. For example, the Egyptians based their calendar on the time Sirius first became visible at dawn, because this meant the annual Nile flood was due.
Sources of Further Information
There are many web sites with information on this subject. Below I have shown some which present the information for both sides of the argument.