Solved! Go to Solution.
Have you tried building a query layer in your map document with only the fields you want to "see"?
For whichever layer it is in your MXD that you are attempting to hide the OBJECTID field for, try creating a query layer instead and specify the fields you do want in the SQL which comprises the query layer. There is a wizard to create the query layers; you'll need to reference the Esri help if you've not found this option in ArcMap before. You might not be required to actually have the source feature class in your MXD in order to create the query layer... I can't recall as it's been a while since I've done this. If you are required to have it in the TOC to build the query layer, just uncheck it before you publish your MXD as a service.