But perhaps a different definition of "reflective" is involved here.

Possibly. A reflective person can use expected-utility to make choices that regular people would simply categorically avoid. (One might say in game-theoretic terms that a rational player can use mixed strategies, but irrational ones cannot and so can do worse. But that's probably pushing it too far.)

I recall reading one anecdote on an economics blog. The economist lived in an apartment and the nearest parking for his car was quite a ways away. There were tickets for parking on the street. He figured out the likelihood of being ticketed & the fine, and compared its expected disutility against the expected disutility of walking all the way to safe parking and back. It came out in favor of just eating the occasional ticket. His wife was horrified at him deliberately risking the fines.

Isn't this a case of rational reflection leading to an acceptance of risk which his less-reflective wife was averse to?