You are half correct. As I understand it:
Healthy people under normal circumstances regulate their breathing based on CO2 since CO2 will rise well before significant decrease in O2.
People with COPD instead regulate based on O2. They are insensitive to CO2 from having had high amounts in their blood for a long time. This is why you have to be careful giving them oxygen since it might downregulate their breathing and cause CO2 poisoning.