is there any possibility to get information/values from hosted ArcGIS Online tables for a locally running python script without using the ArcGIS REST API?
You can use ArcGIS API for Python.
Here is the sample on how to access and manipulate the data in the feature layer:
You could wrap the ArcGIS REST API to provide a more pythonic interface. Thats what https://github.com/Esri/ArcREST did.
I wanted to connect agol to pandas...not stable, just some thoughts: https://github.com/brendancol/agol-pandas/blob/master/agolpandas/agol.py