There was a real and plausible chance that Rand would have chosen that moment to join forces with Lanfear, and to join the Shadow. It was one of the potential futures thrown out by the ter'angreal. If Moiraine had harmed or snared Mierin, there was a possibility that it would have resurrected old feeling in Lews Therin, and caused him to turn - either by helping Lanfear or killing Moiraine. Moiraine almost certainly knew this, which is why she wrote that events had to play out in a certain way. The other alternative that Moiraine saw was that Rand would risk his own safety to help her, and that was the third viewing, where Rand was killed by Lanfear.

Moiraine knew that there was only one way to defeat Lanfear.