Why collect PARTITION statistics on Non-Partitioned tables? - comment by m.tahoon

Thank you Carrie for your feedback.
 
But Based on the explaination in the blog i can't understand how extrapolation will still work with a current statistics for partition/summary.
Let me exlpain my confusion with more details please
Assume we have a products_id table with total of 1000 products distributed evenly between 2 types (500 for each type); tonight loading job added another 1000 product id's also distributed evenly between same product types.
The morning collect stats on partition/summary columns only will update those column with the new row count of 2000 which will match the RAS row count.
in this case the extrapolation will never work since there's no real deviation between row count info. recorded partition/summary column stats and the RAS row count value; however the stats of the [product_type] columns still has info about only 500 products on each type when  product_type column stats had been collected before that loading job.
 
Thank you