update: it may have to do with the parameter "...&returnGeometry=false&..." being passed to the server instead of "...&returnGeometry=False&..." . Could that be the problem?
I'm also seeing this same timeout issue on most of the queries I build. I'm using AGS 10.2 services. It might be that an index is required on any field used in the query. The only query that works for me is one on a field that definitely has an index, so try adding an index.
You know, I never figured the out completely but I found a workaround: when I build the same application and host it myself instead of in ArcGIS Online the problem doesn't exist.