Did you discover a solution to this? Same exact issue here...
I had the same issue, apparently to use the API REST you should have additional permission. interpolation using API REST
The help (Perform analysis—ArcGIS Online Help | ArcGIS ) states:
License:
In order to perform analysis, the administrator of your organization needs to grant you certain privileges. To use any of the analysis tools, you will need the following privileges
Certain tools need additional privileges such as Network Analysis and GeoEnrichment. These additional privileges are noted below in the description of each tool.
Some more links:
ArcGIS REST API: Spatial Analysis Service | ArcGIS for Developers