It did have an error in their convergence proof (which was later rectified by other people). But

• this was only applicable to convex cost functions anyway (General convergence proof in this sense are impossible for general nonconvex problems like neural net training)
• Adam is literally the most used optimiser for neural network training, it would be crazy to deny its significance due to a technical error in a proof in an irrelevant (for this application) regime

Regarding "whatever Hinton was doing": Are you talking about RMSprop? Sure, it's another momentum optimizer. There are many of them.