I disagree. It isn't just "lesser" support. They've only got 30% in favor! As Moderator Rob has pointed out, based on his statistical analysis bids with 50% or less support have all been doomed. Bids with 60% or higher were all on relatively equal footing (in other words there's not any discernible advantage to having 90% public support rather than 65% public support).
No, going back to China won't solve the IOC's PR problem. However, the IOC can easily say, "Hey, we didn't really have much of a choice. They were the best available option. And at least we could reuse a few of the 2008 venues.