Miley Cyrus is claiming > 1%, so your objection to PB does not apply. MC might like to distinguish between 1.1% and 1.0%, but this is minor.

If you're recording claims, not betting at odds, then rounding to zero is not a big deal. No one is going to make a million predictions at 1 in a million odds. One can enter it as 0 on PB and add a comment of precise probability. It is plausible that people want to make thousands of predictions at 1 in 1000, but this is an unimportant complaint until lots of people are making thousands of predictions at percent granularity.

An advantage of PB over bilateral bets is that it encourages people to state their true probabilities and avoid the zero-sum game of setting odds. A well-populated market does this, too.