The article is slightly vague on this point. It says NV/WY/NM "don’t require corporations to record their owner", but that is not really accurate.

The owners are recorded when the LLCs are filed with the secretary of state, however these states are simply willing to keep the identities of the owners private, without publishing them as most other states do. As in most other states, you do need a Registered Agent, but you can delegate this to an attorney or company who serves to receive legal notices, correspondence, etc.

If there is any type of law enforcement investigation of the company, police would simply go to the secretary of state to determine the owners.

Not all Corp credit cards record the name of the person registering them. The ones my company uses are all tied to the company and we internally manage keeping up with who has what.