I love that documentary and Helen Castor's work. In my classes on Tudor history we touched on Jane Grey briefly. For the most part, Lady Jane is tricky because it's difficult to confidently place her in the timeline of the British Monarchy because of the circumstances of her short rule. She was named the heir by Edward over his two sisters and on his death was the first proclaimed female monarch but she was never coronated and so was never officially Queen because Mary was able to claim the throne after 9 days. It's kind of how Charles is now, he's effectively king but he's not officially king until he's coronated. No one who already had power wanted Mary, who was Catholic, or Elizabeth, who was considered illegitimate since Anne Boleyn was accused of infidelity to sit on the throne. It's also difficult to know how much agency Jane had in the decision especially since she was still a teenager. She was married to the son of Northumberland who was acting as a sort of regent while the young king was ill. Putting Jane on the throne would ensure he kept his power and that his own son became king as well. (This isn't to say Jane was weak, as a Tudor, she was very well educated and wasn't afraid to express her own opinions) The document that named her heir also only named the males born to Jane's mother Francis and then Jane and then her sister Margaret so the women were really only placeholders until a boy was born. This was true until Edward changed it at the last minute to also include Jane herself when it became clear that there would be no male heirs before succession had to be solidified. The succession was never publicly announced and Jane was never even informed that she was made the heir. This surprise made the public sceptical of Jane as a Queen as Henry VII named Mary and Elizabeth as his heirs so naturally Mary should be the Queen. The documentary mentions a couple of times how going against the natural order of successon would be seen as too chaotic and nit reflect well on Jane. Jane is a tricky subject because she was only technically an heir and not publicly named, didn't have the best claim to the throne both through parentage and the fact that when she was named queen her mother was still alive (who should have been named as the one higher in the line but wasn't made heir in that document), and was probably forced into the role by people who wanted to control the throne through her. You can pick a stance on whether or not she should be considered a true queen and you could argue your stance with the evidence we have but there's just as much evidence the other way as well.

ETA: all of this information is in the documentary so I know none of this is new to you. The answer to your question comes down to how much strife surrounded Jane and her time as queen and how that makes it difficult to tell her story. You can even see it in the interviews they do where some people believe she was just a pawn of Northumberland and some believe she was in control of what was happening.