This was my thought exactly. If I was given the option to keep the rest private if I lost, 1A would be a distinctly preferable choice. If I had a 1/34 chance of having to explain how I "lost" $24,000 vs an average loss of $2,200, I might well take choice 1B. (at a later time in my life, when I could afford to lose $2,200, and had significant financial risk from being perceived ask a risk-taker with money).

I think these kinds of 'side channel' loss information are what make your intuition value 1A > 1B. In a way the implicit assumptions in the offer are what cause the trouble. Naive subjects are naive only to pure math not to real life.