The vast majority of yes/no questions you're likely to face won't support 5% intervals.

I agree [edit: actually, it depends on where these yes/no questions are coming from] , but think the questions I was looking at were in the small minority that do support 5% intervals.

Not "true, 60% confidence" (implying 40% unknown, I think, not 40% false)

Perhaps I should have provided more details to explain exactly what I did, because I actually did mean 60% true 40% false.

So, I already was thinking in the manner you advocate, but thanks for the advice anyway!