And of course totally ignored the Act of Settlement by which parliament decided the fate of the crown.
(A) Even people with only a glimmer of knowledge of British history know that the present monarchy is not the senior line, that in fact parliament passed over 50 plus people with stronger blood claim to specify that future monarchs would come from Sophia of Hanover.
(B) Given that this Queen is the correct descendant since 1714, you know that someone else is the true senior line. Before watching the TV show you just didn't know who was that person.
(C) If genealogists have tracked 2.3 million different bloodlines from William the Conqueror to Prince Williams, the idea that they lost track of the senior male preference primogeniture line is ludicrous. The TV show tries to sell the idea that if it wasn't for Tony Robinson's research the bloodline would have remain undiscovered. In reality, it was a well known bloodline to genealogists that Tony Robinson made famous to the general public.
(D) The fact that the bloodline from George Plantagenet, 1st Duke of Clarence made the Tudors nervous is also part of every textbook. Henry the 7th and Henry the 8th managed to kill the first three generations in some of the most famous executions of the Tudor era. The execution the last of the direct line Plantaganets was a priority for Henry the 7th. The execution of the Catholic martyr, Margaret Pole, is front and center in every story of Henry the 8th. With the Stuarts taking control of the monarchy, the alternative bloodline began to fade in importance.
(E) The politics of the TV show bothered me a lot. Had they made the TV special a few years earlier it would have ended with an old countess, who faithfully sat in the House of Lords for decades, guarding her family heritage, even though the money was completely lost in the early 20th century. By waiting until she died, they could end the search with her son, who had run away to the Australian Outback as a teenager, and was a dedicated Republican. You get the feeling that Tony Robinson, a dedicated republican, was waiting for the mother to die.
(F) The implication of the TV show that it ended in a "King Ralph" scenario, where some poor fat slob is told that he is now the British King. While Michael lived in a little house in the Australian Outback, he knew that he was an Earl, and he knew his bloodline. He couldn't help but notice that his surname, "Hastings" was one of the most prominent in English history. At one point he complained about his mother and aunt being obsessed with the bloodline and trying to regain the titles that had been lost over the years.
===============
All that said, I did enjoy the TV special, and I encourage you to watch it. It does provide an interesting view of history, the acquisition and loss of great family fortunes, and the politics of Britain throughout the last centuries. Keep in mind a few things:
(1) Henry the 7th was king primarily by Right of Conquest. The status of his wife was important to the politics of keeping the peace at the end of th 15th century.
(2) Male preference primogeniture (MPP) was a system that evolved with many bumps. King John, murdered his nephew to defeat his rival claim to the throne. Today the nephew would be king. Applying MPP backwards throughout centuries back to William the Conqueror is an exercise in logic, not an alternative history
(3) According to English common law, if you raise a child as your own, it is your own. Illegitimacy cannot be claimed years later, or especially posthumously.
In general I enjoy alternate histories. It makes you wonder about crucial moments in time, and how they can change everything.