I don't think I've ever heard of anyone speculating that Elizabeth might have been involved with what happened to Mary in a conspiracy-theorist, eminence grise way. It wouldn't make a lot of sense? None of what happened to Mary was "coincidental". The vast majority of the issue with Mary Stuart was the divide between Catholics and Protestants - the Scottish royal family had been Catholic, she went to Catholic France as a child and remained committed to the Catholic cause against (what they saw as) heresy, while the aristocratic Scottish population steadily became more Protestant.

Mary's mother, Marie of Guise, had been struggling for some time against Protestant Scots who didn't wish to be ruled by a Catholic or have any French interference. Marie had initially struggled with the Earl of Arran, the official regent for Mary while she was in her minority, and in so doing she had given more power to the Protestant lords; then the Protestant Queen Elizabeth came to power in the next country over, and the Protestant agitators like John Knox came back to Scotland, and there was a crisis on her hands. English and French-Scottish forces would clash repeatedly, resulting in Marie first signing a treaty to allow some tolerance of Protestants in Scotland, and then fleeing as the Scottish and English forces united against the French. Henri II of France then died, leaving his son François (Mary's husband) as a new and inexperienced king, while the powerful Guise presence in the French government was provoking its own problems against the Protestant Huguenots and became more reluctant to help out with Scotland.

Marie of Guise died in 1560, leaving the Scottish Protestants in charge of the country. The Protestant lords negotiated with England and France to end the war between their countries and produce a result that was beneficial to all except Mary: the lords would rule Scotland, Mary would no longer claim Elizabeth's title, if there was any more trouble form that quarter the English could invade, and all foreign troops would leave Scotland. The lords, now fully in charge, followed up by outlawing Catholicism and sacking monasteries, much like what had happened in England under Henry VIII.

This was followed quickly by the death of François, which made Mary a teenaged dowager and Catherine de' Medici regent for her younger son, Charles. Catherine was an enemy of the Guise family and wanted to be rid of Mary, who was one of them; she also did what she could to prevent Mary from making a powerful royal match with Spain to keep her and therefore the Guises off the political stage. Her only real choice was to go back to Scotland despite the risks and claim her own country, or to completely sink into powerless retirement.

Things seemed all right for her when she returned to Scotland, as she said she'd make no changes to the lords' religious program, but she continued to hear mass privately, which was an issue for the more intolerant Protestants like Knox. BUT. Mary refused to ratify the treaty that proclaimed Elizabeth the rightful ruler of England and Ireland, and didn't at least name her Elizabeth's heir. While today it seems preposterous for anyone to claim to be more Queen of England than Elizabeth I, now an absolute symbol of English power, from Mary's perspective she was absolutely right to do so. Without a papal annulment for Henry VIII's marriage to Catherine of Aragon, his marriage to Anne Boleyn was invalid in the eyes of Catholics and Elizabeth illegitimate; likewise, Henry VIII and Edward VI had no right to disinherit Margaret Tudor's descendants for not being heretics. This isn't a case of pressing an ambitious claim based on ancient lines of descent, but a living, breathing controversy. Elizabeth was obviously not inclined to step down in favor of Mary, and even conceding that she would be the next Queen of England was too problematic to countenance: the popular Mary would be a rallying point for English Catholics (which there were still many of) and a potential usurper before Elizabeth's death. Things got worse as the Guises cracked down horribly on Protestants in France, which made Elizabeth even less willing to trust Mary or at least show her public favor.

So I would guess that the things you're asking about Elizabeth having a hand in would be certain events which occurred after Mary returned to Scotland and refused to concede her claim. In 1562, the son of the Earl of Arran confessed to Mary that he and the Earl of Bothwell were plotting to kidnap and rape her until she allowed them to take over the government. (His father claimed that he was mad and that the plot was entirely Bothwell's.) Later that year, the son of a disaffected noble, the former Earl of Moray, whose title Mary had given to her half-brother, threatened violence against her escorts and a forced marriage for her, and she and her men had to fight their way to safety. In early 1563, a poet named Pierre de Bocosel de Chastelard hid under her bed once and burst into her bedroom on another occasion, after which he was executed. There's no evidence I'm aware of that Elizabeth was involved with any of these attempts on Mary's person - but these aren't coincidences either. They're a result of the misogynist norms of the time. While it wasn't still the norm by the 1560s for men to actually abduct heiresses and the like to force them into marriage, there was very much a sense that such women were fair game for men who wanted to gain power by marrying them. (Though Chastelard was probably more akin to a modern stalker than someone actually trying to gain the throne of Scotland.) Likewise, Mary's later issues with marriage also tied into this problem. Lord Darnley was Mary's choice to take herself out of play as a potential marriage for any Scottish nobleman who fancied a try, and after Darnley's murder, Bothwell did in fact enact the plan to force Mary into marriage. The marriage with Bothwell would eventually result in Mary's abdication, escape, and eventual imprisonment by Elizabeth for what was intended to be an indefinite period of time.