No, there isn't conflicting information in BoL, just careless reading of BoL information. The list of 6 endpoint types includes HTTP endpoints, and it is clearly stated in the paragraph immediately after the list that all HTTP endpoints are user created not system (default) endpoints (and don't show up in SQL Server Configuration Manager); each of the other 5 types has one system endpoint created during instance installation whether or not the relevant protocol is enabled (not all protocols are enabled on installation), and these 5 are the only system endpoints of the instance.

Since I tend to favour web services as a way of getting from client to server in some circumstances and TCP in others the first endpoint types that sprang to mind were HTTP and TCP so I counted two there and then added one each for shared memory, named pipes, VIA and DAC to get six, forgetting that HTTP doesn't count because there is no system http endpoint, and ending up with the wrong answer - no points for me this time, although I not only should but also do know better.