Thank you for the answer.
I am not sure you've got me right though. A model with the Truncate Table tool I publish as a GP service is able to edit a feature class regardless where it is stored - in a file geodatabase or an ArcSDE geodatabase. Nothing is copied to the server ever (I have data store registered). However, it seems as the GP service can truncate only the feature class I've used when running the model first for generating a successul result (in order to publish it). So the GP service does truncate the same feature class over and over again regardless of what I choose as my input table when running the GP task. My aim, however, is to be able to specify any feature class (that is accessible to the server of course).
So, when publishing a model as a GP service and specifying "User defined value" as the Input Mode I am not able to run the GP task - getting this "000187: Only supports Geodatabase tables and feature classes" error. However, when specifying the Constant value during the publishing process, no parameter for the GP task is created and the GP task runs successully yet of course with the same feature class I've run it in Desktop first. I want to find a way to leave the input feature class as an input parameter for the GP task and be able to run it successfully.
What puzzles me is how to make the GP task work on a user provided feature class from a registered data store instead of using a constant feature class that I've run the model with to be able to publish a successful result.