We are splitting hairs here. Something can be both assur and not bekovidig. In sports, before certain performance enhancers became formally assur they were first not bekovidig.
Here is another example: A former President earns $10 Million a year in speaking engagements. It is perfectly legal, but it lowers the status of the presidency. Begging or relying on government assistance is not assur, but it surely is not bekovidig.