Question: Some say that ignored risks as part of an organization's behavior are much worse than accepted risks.

I would like to test that axiom (in the eyes of some).

When I am handling a risk and I choose to accept it, it means that I have done risk analysis and risk control, and have chosen to accept this risk and to live with it.
When I am doing the same thing, only this time I choose to ignore that risk, am I not doing the same thing? I am living with that risk as part of my operational plan as an organization.

Some would say that it is foolish to ignore risks. However I am seeing it this way - The only difference between an accepted risk and an ignored risk, is the mere fact that what I am accepting a risk, I am keeping myself and my organization self-aware to that risk. And if a risk is ignored, then I probably ignored it because it is a lightweight risk, the chance of it being leveraged is minimal, and the costs of the vulnerability associated with it being exploited is zero to none.

So, is the difference so big?

Answer: 
In the context you have described, there is no such thing as an ignored risk. What you have outlined is risk acceptance. 

If you weigh up the risk and decide not to do anything, you are accepting that risk, not ignoring it.
I accept the risk that I may die in a car accident.

The convenience of the car is great enough that I continue to drive it.

The risk of death is low enough that I have decided the existing measures (air bags, seat-belts) are good and no other measures (jump jets) are worth the cost they require. I will periodically check to see if any new measures are introduced.

I would not describe this attitude as foolish because a reasonable evaluation of vulnerability was done. Mitigation costs and benefits were considered and rejected. And a commitment to periodic re-evaluation was made. 

I do not know about the asteroid that will impact and destroy my car. 

Have I made enough inquiries into threats and vulnerabilities and failed to detect the asteroid threat?

Or was my research insufficient to uncover threats and vulnerabilities for which reasonable mitigations exist?

I think the last question can help you decide if you are truly ignoring risk.