Facebook has developer APIs but they, ultimately, control the ecosystem. They only let developers kinda play in it. I honestly don't think Twitter needs to win any developers back for two reasons.
1. They should be more like Facebook. Never, ever again allow a third party app to control the primary way to view all of their data. It's too important. Grandfather existing apps in but slowly add new capabilities that they cannot access thus smothering them.
2. If Twitter can become more engaging / sticky it can keep users around for longer which should, in theory, help bring more people to their platform and let them display ads longer. This will ultimately force developers to work with them again, regardless of their feelings around trust.
Look at Facebook. They destroyed many games livelihoods with changes and people not only still use them but other than places like HN you rarely hear about issues with developers trusting them.