Exactly. Take a more extreme case:
“Linda is single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with the issue of discrimination and social justice. Which of the following is more probable: Linda participates in Neonazi rallies, or Linda participates in Neonazi rallies as a undercover mole?
Clearly when phrased that way, it seems to imply that the first half of the conjunction refers to participating in Neonazi rallies not as a mole, even though the logician says “Bwa ha, that’s not what I said!”
