She talks you into doing some weird Elven traditions cuz she just loves history so much and maybe it's important.
You forgot about her lying to you about what was actually written on the tablet, until it became convenient for her to tell you.
Uh...no. And I even think there is the possibility of killing Abelas in all that, which would have made this scene even more different for me my first PT. So, yes, Bioware is depending on you, the player, to have previous knowledge of Morrigan to make that trust leap and let her drink.
There's also the possibility that she abandoned the Hero on the eve of battle against the Archdemon, and Leliana might be able to confirm that her reason for leaving was that she was denied power.
In my first play through, it backfired, because everything I knew about her made her more suspicious, not less so, even though my Warden loved her as a sister. But there are hundreds of good reasons a character could also choose to let her drink or not drink that doesn't depend on our knowing her as a character.
My first PT Human Mage drank, being too suspicious of Morrigan to not do so.
For mine it came down to the compulsion. He ran through the list of others who might drink, Solas, then Vivienne. Then when Vivienne suggested the Inquisitor he turned and said, okay I don't know who would be better suited to drink.
But then later when he and Vivienne talked about Morrigan betraying them, he told her he doesn't think it's just a possibility, he thinks it's a certainty.