Just curious to know if you every got this question answered?
You don't use the "map service" in the webmap, you need to use the "feature service". Collector only shows "feature services" which are the editable services.
You would need to use the URL of the rest point for the feature service and add that "From the web" when putting content on ArcGIS Online. So it would be something like yourserver/rest/the_service/featureservice.
You can add a feature service to the webmap and make the service not editable in AGOL - see the options menu for the layer in your AGOL map.