I believe you are encountering a bug:
[#NIM084962 The ArcGIS.com map viewer does not allow editing of ArcGIS Server feature services from an internal network when using Internet Explorer. ]
The workaround is to edit through Chrome or Mozilla Firefox.
Download the Firefox web browser and it should allow you to edit. You should also be able to edit using Collector or the old ArcGIS (green) app. I had the same issue at my previous employer. The security settings in IE (and possibly Chrome) were to blame. I had editable feature services on our internal Arc Server that I brought into my AGOL web map and got the same error. The other option is to publish as a hosted feature service on AGOL.
Not sure of the version, but this was last year - mid 2014. There were some proxy settings that our IT dept. had set that I could not change, but I never got the specifics. Sorry I can't be more help.