Nice to see you here! Overlapping channels such as 1 and 2 could actually arbitrate with each other if they were close enough together. This can be easily proven by performing a packet capture on Channel 1, and you will see traffic from Channel 2.
If the Cisco paper says channel 1 and 4 can arbitrate, that MAY be true, but only in such close quarters that it would be highly unlikely that the situation would exist. If the network is properly designed, channel 4 would be non-existent.
To the OP, don't worry about the section that talks about arbitration on overlapping channels. That is way too much information when trying to learn CSMA/CA.